Spurs agreed a EUR60 million (PS50.
2m) fee with Bayern on Thursday but the deal was dependent on whether Tel accepted the offer from Ange Postecoglou's side.
Spurs chairman Daniel Levy travelled to Munich on Friday to put forward the club's proposal but Tel turned down a move to Ange Postecoglou's side and told Bayern he would rather stay if no other teams come forward before Monday's transfer deadline.
According to RMC Sport, only United and Arsenal remain in the running to sign Tel and would be able to convince the 19-year-old to leave Bayern before the end of the January transfer window.
The report adds that Chelsea and Aston Villa are now out of the race for Tel.
Sky Germany report that United have spoken to Bayern on the phone about a possible deal for Tel but have yet to come forward with an concrete offer.
Earlier this month, Chelsea made their approach but it's understood that Tel is reluctant to move to Stamford Bridge due to the strong competition for a place in Enzo Maresca's side.
Tel's primary reason behind his desire to leave Bayern is down to his lack of playing time having started just three matches for Vincent Kompany's side this season.
Speaking on Wednesday night, Bayern's sporting director, Max Eberl, revealed that Tel had asked to leave the club having initially asked to stay.
'And now we have to think about what we are going to do, whether we are going to do it.
'The playing time is not satisfactory for him, and that is understandable.
'It is now the end of January.
And now it is more difficult for everyone involved.
We have to see what is ultimately best for everyone involved, for Mathys and for Bayern Munich.
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