Spurs chairman Daniel Levy rejected Chelsea's £40million offer for the Croatia midfielder in the closing days of the transfer window but the Blues are in no mood to give up their pursuit of the player.
However, they are set to face competition from United when clubs are allowed to trade again next year.
United were interested in Modric, who had made his preference for Chelsea clear because he would like to stay in London, during the summer but he was not their first-choice midfielder.
However, the 25-year-old has now moved up the pecking order. United's principal target in that position was Samir Nasri, who chose instead to join their rivals City. They were also chasing Wesley Sneijder but when Inter Milan sold Samuel Eto'o to wealthy Russian club Anzhi Makhachkala, there was no pressure on owner Massimo Moratti to cash in on the Dutchman, whose weekly wage is above £200,000.