The summer transfer window may have drawn to a close but that doesn't necessarily mean the Premier League's top clubs have suddenly stopped all transfer activity.Indeed, sourcing new talent is an endless enterprise in the modern game, with scouts, agents and club representatives working all year round to try and find the best transfers possible for their respective employers.With that in mind, Football Fancast are taking a look at summer targets some of the Premier League's biggest teams haven't given up on just yet, despite the window slamming shut at 6pm on Monday evening.This article focuses on Arsenal, who will be under huge pressure to splash the cash when the transfer window reopens in the new year. They finished the summer as the only club across Europe's leading top flights not to sign an outfield player, much to the disappointment of the fan base.So with that in mind, here's FIVE Gunners transfer sagas that will continue into the January transfer window. Enjoy!

KARIM BENZEMA

Arsenal spent much of the summer chasing Real Madrid's Karim Benzema only to eventually receive an emphatic 'no' from the striker via Twitter:

But the situation could swing in Arsenal's favour by the time the transfer window reopens in January, especially if Rafa Benitez comes good on his apparent plans to utilise Cristiano Ronaldo as a lone centre-forward this season - leaving the France international to linger on his subs bench.

Even so, Arsene Wenger is hardly known for splashing the cash in January, so he may decide to wait until next summer before launching a bid for the £46million-rated 27 year-old.

SIMONE ZAZA

A cheaper and shorter-term solution to Arsenal's lack of firepower, the Gunners have already been linked with a follow up bid for Juventus forward Simone Zaza after reportedly coming close to signing him on summer deadline day.

He’s amassed an impressive 49 goals in 117 league appearances throughout spells with Viareggio, Ascoli and Sassuolo, prompting Juve to repurchase the 24 year-old from Sassuolo for €18million in July – a clause inserted into Mapei Stadium transfer last summer.

But he's yet to make a competitive appearance for the Old Lady, stuck behind Alvaro Morata and summer signings Paolo Dybala and Mario Mandzukic in the pecking order, leading Arsenal to inquire into the Italy international's availability as the transfer window drew to a close.

In typical Wenger style, the north London outfit apparently baulked at his £22million price-tag. But The Guardian believe a loan move in January is still a possibility - providing Arsenal are willing to pay Zaza's wages and a £1.4million loan fee.

GRZEGORZ KRYCHOWIAK

How much interest had in Sevilla enforcer Grzegorz Krychowiak this summer remains open to interpretation. As explained by HITC, the English media describe it as a 'passing interest', whilst their Spanish counter-parts allege firm enquiries until the final days of the transfer window.

But there's no doubt Arsenal still need a holding player, with Francis Coquelin now the only dependable ball-winner in the Gunners' engine room, and the Poland international has emerged as one of Europe's best since moving to Ramon Sanchez Pizjuan last summer.

Indeed, he averaged 3.3 tackles, 3 interceptions and 3.4 successful aerial duels per match to earn a place in La Liga’s Team of the Year for 2015, whilst helping Sevilla claim a second consecutive Europa League title.

The bad news is that the 25 year-old is set to sign a new contract with the Spanish outfit likely before the end of the international break. The good news, on the other hand, is that his £21.4million release clause won't be increased - suggesting the Gunners could turn to him in January if Coquelin fails to sustain last season's impressive form.

ADRIEN RABIOT

According to The Daily Mail, Arsenal made a last-minute enquiry into the availability of PSG prodigy Adrien Rabiot, by no means an audacious claim considering the Gunners' need for a holding midfielder and Arsene Wenger's eternal lust for young talent - particularly young French talent.

The 20 year-old is widely regarded as one of world football's more exciting midfield prospects, having already played a significant role in PSG's last two Ligue 1 titles and amassed 91 career appearances in total - in addition to representing France at youth level on 41 occasions.

It seems PSG weren't interested in selling Rabiot, who has been valued as highly as £21million by the tabloids in recent months.

But the midfielder's mother and agent, Veronique Rabiot, kicked up quite the fuss about the France U21's limited playing time over the summer, at one point allegedly making a transfer request on behalf of her son.

So if the 6 foot 2 defensive-mid continues to be overlooked by Laurent Blanc - which seems likely considering PSG snapped up Benjamin Stambouli and kept hold of Thiago Motta this summer - we could see him push for a move away in the new year.

WILLIAM CARVALHO

Sporting Lisbon star William Carvalho is destined to join a top Champions League club at some point in his career and the chances of doing so seemingly increased after he claimed the Player of the Tournament award at the summer's U21 European Championship.

The midfield enforcer, who measures in at 6 foot 2, weighs in excess of 14 stone and is famed for his simple-yet-effective play-breaking style, has been mooted as an Arsenal target for some time and scouts allegedly watched him in action during the tournament's final.

Despite the Gunners' need for a holding player, their much speculated follow up bid - having reportedly made a substantial offer on deadline day 2014 - never materialised.

But that could be due to the 23 year-old picking up a stress fracture on his tibia in July, which has ruled him out of action until October at the earliest.

When fully fit we could see the north London outfit launch a bid - but linked to Manchester United and Real Madrid, to name a few, there will be plenty of competition for Carvalho's signature.