The Algerian forward is currently on loan at Monaco until the end of the season, but both clubs are believed to be interested in signing him this month.
According to RMC Sport, United have been in contact with Slimani’s representatives over a switch, while Spurs have also made enquiries.
Though as yet it is unclear whether either club want the 31-year-old on loan or a permanent transfer.
Slimani has enjoyed decent form in Ligue 1 this season, scoring seven goals and providing as many assists in 11 league starts.
However since the arrival of new boss Robert Moreno at the end of December, Slimani has played just 30 minutes of first-team action.
Both United and Spurs are short on strikers following the injuries to Marcus Rashford and Harry Kane.
Leicester’s Jamie Vardy has also been struggling with a muscular problem, though it is not as bad as first feared, and the Foxes are not considering recalling Slimani.
They are keen to recoup as much of the £30million they paid for him in 2016 though, but realise they will have to make allowances, given his age and the fact his contract ends in 2021.
It is thought United and Spurs only consider Slimani a short-term option, and therefore would be hoping to take over Monaco’s current loan of the player.
United have faced a frustrating window, with the transfer of Sporting Lisbon midfielder Bruno Fernandes continuing to drag on.
Both clubs are currently some way apart in their valuation of the player, and Sporting boss Silas admitted Fernandes could still be with the club beyond Friday’s deadline.
“Right now I don’t know if he will stay or not, but I would like to count on him at least until the end of the season,” Silas said.
Tottenham meanwhile have been fairly active in the window, signing Gedson Fernandes on loan from Benfica, while PSV’s Steven Bergwijn is expected to join for £30million.
Danish midfielder Christian Eriksen is set to complete his move to Inter Milan for a fee in the region of £16.8million.