The Red Devils are looking to bolster their midfield after completing the record signing of Harry Maguire from Leicester.
And Spurs could sell as they’re desperate not to lose Eriksen and Toby Alderweireld on free transfers next summer.
Both have entered the final year of their contracts and Tottenham would be tempted to cash-in this week.
The Manchester Evening News claim Spurs were ‘gutted’ that United didn’t make a move for Alderweireld earlier in the window.
The Belgian had a £25m release clause in his contract which expired on July 25.
Manchester United have shown interest in Eriksen in recent months but are cautious about dealing with Tottenham chairman Daniel Levy.
Dimitar Berbatov back in 2008 was the last player that moved from Spurs to Old Trafford.
Sir Alex Ferguson famously said negotiations with Levy were ‘more painful than a hip replacement’.
Eriksen underlined his desire to leave Tottenham at the end of the season with Real Madrid thought to be his preferred destination.
“I feel that I am a place in my career where I might want to try something new,” he explained.
“I have the wildest and deepest respect for everything that has happened in Tottenham, nor will it be negative.
“But I have also said that I would like to try something new.”
Back in 2012, Eriksen was keen to join United but Ferguson opted to sign Shinji Kagawa instead.
There are also suggestions Real Madrid want Tottenham to entertain United’s efforts as they monitor Paul Pogba.
Los Blancos are interested in the World Cup winner and could make another attempt to sign him should Eriksen move to Old Trafford.
Eriksen was in good form again last season for Tottenham, netting 10 times and providing 17 assists in all competitions.