Manchester City have already been heavily linked with the pair, and now reports in the press suggest that United boss Jose Mourinho has also joined the hunt.
Spurs will be desperate to keep hold and will be under no pressure to cash in after both players signed bumper new five-year contracts at White Hart Lane last year.
It has also been claimed there are no release clauses in either deal, meaning that United or City would have to pay big bucks to have any chance of luring them away.
Spurs chairman Daniel Levy does not want to sell to a club also chasing Premier League glory, but a £60million double bid could test his resolve to the maximum.
Whether Walker and Rose would consider a move away also remains to be seen, as they may view a move to United in particular as a sideways step at this moment.