According to Rob Dawson of ESPN FC, Spurs could be open to negotiating on the £130 million price tag they initially quoted when Eriksen said he wanted to leave the club earlier this summer.
Eriksen, 27, has only a year remaining on his contract at Spurs, so they risk losing him in a cut-price deal in January or for free next summer if they do not sell him in the current transfer window.
Per Dawson, club chairman Daniel Levy is "reluctant" to let that happen.
United are lacking in the centre of midfield after losing Ander Herrera to Paris Saint-Germain.
Marouane Fellaini also left Old Trafford at the beginning of the year to join Chinese Super League club Shandong Luneng.
Paul Pogba, Juan Mata, Andreas Pereira and Jesse Lingard can all operate in advanced central midfield roles, but arguably none can offer the same kind of skill set that Eriksen could.
Pogba is supremely talented, but he prefers to play a little deeper than the No. 10 role Eriksen favours, and both have been linked to Real Madrid:
If Pogba were to stay put at Old Trafford instead of moving to the Santiago Bernabeu, the Denmark international would still be a superb signing, and the pair could likely work well in tandem:
Eriksen's creativity is his major asset. He has reached double figures for assists in each of the last four Premier League seasons, setting up a combined 50 goals in that period while scoring 32.
That kind of return could be a huge help to United as they aim to return to the Premier League's top four.
In each of the six Premier League seasons since Sir Alex Ferguson left the club, United have failed to pass the 70-goal mark.