He's been in impressive form so far this season, scoring seven goals and assisting a further seven in just 13 league appearances.
The report states that the two English sides are in conversation with the Algerian's representatives.
The deal is somewhat complicated because of Slimani's existing contract with Monaco.
But if he can be convinced to join either United or Spurs, a deal could be done with Leicester for the said club to take over Monaco's loan.
Otherwise, either club could bypass the loan dilemma and make a bid to purchase Slimani from Leicester outright.
Leicester bought Slimani from Sporting Lisbon in 2016 for £27.5m as part of their league-winning outlay.
But in 18 months at the Foxes, he failed to assert himself and joined Newcastle on loan - which would be the first of three loan spells.
Both United and Spurs are known to be hunting for a striker this month.
The Reds suffered the loss of an in-form Marcus Rashford to injury and he's not expected to return till the latter stages of the season.
Similarly, Spurs talismanic captain Harry Kane was ruled out till at least April with a severe hamstring problem.
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