Red Devils manager David Moyes is believed to be ready to dip into the transfer market this month in a bid to boost his squad after a disappointing opening half of the season.
With defeat at the hands of Tottenham, the Scot’s side are now 11 points adrift of leaders Arsenal, and five away from Champions League qualification.
Although midfield reinforcements are believed to be the priority for the start of 2014, Moyes is also on the lookout for a new backup stopper with current number two Anders Lindegaard expected to leave Old Trafford in search of regular playing time.
Gunok has emerged as a candidate for the role, with the 24-year-old having impressed in his native Turkey.
The glovesman is a product of Fener’s youth set-up, and has featured for their first-team since 2009.
Reports suggest that a £1.5m offer is being readied by United, who are keen to tie up a swoop in the coming weeks.
Gunok is highly-rated in his homeland, and has already made five senior international appearances.