The Daily Mail claims that the Spurs will refuse to let their star man leave for less than £35 million, a development that was expected given that Tottenham rejected a £40 million offer from Chelsea last summer.
Meanwhile, Tuesday's Mirror reports that cash-rich Paris Saint-Germain have entered the race to sign Modric and will offer in excess of £30 million, significantly more than the £22 million it is said United put forward.
United could also be set for some entrenched negotiations over their reported pursuit of Borussia Dortmund striker Robert Lewandowski. Last week, in comments that were likely misinterpreted, several news outlets led with quotes from Poland coach Franciszek Smuda appearing to suggest that Lewandowski was heading to Old Trafford.
But Dortmund chief executive Hans-Joachim Watzke has said that there is no chance their leading marksman will be leaving the Westfalenstadion this summer.
It does not matter if we are to receive bids, he told Sportinformationdienst.
I have said for weeks that Robert will be back in training with our club after the Euro 2012 and his holiday leave. And this is what will happen.
While United will feel that Lewandowski is still potentially within reach, one player not likely to be heading to the 19-times league champions anytime soon is Karim Benzema.
Faced by the British press, before France's match with England on Monday, the striker was, of course, asked about the chances of a move to Premier League. It is widely known that Sir Alex Ferguson made a concerted effort to sign Benzema when he left Lyon for Real Madrid three years ago. And, says Benzema, that interest has not waned in the intervening years.
I am very happy at Real Madrid, and the thought about leaving has never crossed my mind, Benzema said, according to Sky Sports. I know Manchester United have tried to sign me for the past three or four seasons.
When I was at Lyon they and a number of other English clubs wanted me but could not agree terms with Lyon. Besides, I wanted to go to Spain and I can honestly say I have never regretted that decision.
According to the Manchester Evening News, United remain interested in signing left-back Leighton Baines, but could face competition for his signature from Napoli. A development that will likely frustrate United's efforts at the negotiating table.
Various reports have stated that, while Everton remain steadfast in their assertion than Baines will not leave for anything less than £20 million, Ferguson is not willing to go above £15 million.
Even that reduced figure seems a lot, though, for a 27-year-old who is likely merely to provide competition for experienced regular Patrice Evra. If indeed the purse strings are tight at Old Trafford, expect Ferguson to go for a younger of cheaper option. As has been seen over the years, there is little value in buying English players.