Slater spent last season on loan at the MKM Stadium, helping Grant McCann’s side win promotion from League One before returning to Bramall Lane.
McCann would like to sign the 22-year-old on a permanent basis, after first expressing an interest in pushing through a deal during the summer transfer window.
Although that came to nothing, the Northern Irishman has continued to monitor Slater’s situation closely and hopes to finally broker an agreement later this month.
However, McCann admitted he has yet to hold detailed talks about the future with Ilicali following Wednesday’s victory over Blackburn Rovers.
Slater, whose contract with United expires at the end of the season, is expected to wait until City remove the uncertainty surrounding their managerial position before reaching a binding decision about the future.
Wigan Athletic are also known to admire the youngster, who was an unused substitute as Paul Heckingbottom’s men drew with Preston North End on Tuesday night.
Hailing from Gleadless, Slater progressed through United’s youth programme before making his first team debut during an EFL Trophy tie against Grimsby Town in November 2016. After scoring in that match, he then made his league debut at Deepdale a year later before making what could be his final United appearance at Ipswich Town in the 2018 FA Cup.
Slater also enjoyed spells on loan with Carlisle and Scunthorpe ahead of his switch to City. He made 34 appearances there, scoring once.