The Reds have already been extremely active in the summer transfer market, with Christian Benteke – their last addition – number seven in what has been a busy few months at Anfield.
It was thought that the business on Merseyside would end with the signing of the big Belgian, however, with Lucas Leiva edging towards a move away from the club, Illarramendi is now a target.
Reports claim the Spaniard – who has been compared to Kop idol Xabi Alonso in the past – is wanted, with his deep-lying passing ability making him a good replacement for departed captain, Steven Gerrard.
Cheryshev is also thought to be a target, with the Russia international a ready-made replacement for Raheem Sterling – now a Manchester City player.
However, with Brendan Rodgers already possessing the likes of Jordon Ibe and Roberto Firmino a move for the former Villarreal loanee appears to be more unlikely than a swoop for Illarramendi.