The Croatian, a £30 million signing from Tottenham in the summer, has failed to impose himself in Spain and Marca readers this week voted him the worst Liga signing of the season.
Modric has received much blame for Real Madrid's floundering first half of the season and has only started eight Liga matches.
He told Croatian newspaper Sportske: "This is Real Madrid. I understand there is great pressure for new signings to succeed here.
"I'm not making excuses, I am not that kind of person, but it is very challenging to adapt to life at a big club like Madrid."
United and Chelsea both tried to sign the 27-year-old from Tottenham in the summer, but Spurs' reluctance to sell their star man to Premier League rivals ensured he went abroad.
Chelsea see Modric as the perfect replacement for Frank Lampard while United's central midfield issues are well-documented. City may see Modric as the man to restore creativity to an attack that has stuttered this season.
Chelsea are closing in on the £15 signing of Malaga playmaker Isco, the Sunday People claims.
The Spain Under-21star has been one of the key performers in Malaga's impressive Champions League run, and would be Rafa Benitez's second major acquisition of the January transfer window after Demba Ba.
The Sunday People also claims that the club are preparing to make a U-turn over Frank Lampard's contract, and could offer the 34-year-old an extended deal at Stamford Bridge.
Real Madrid, meanwhile, are preparing a £50m bid for ex-Atletico man Sergio Aguero, who may seek a return to Spain from Manchester City following the break-up of his marriage to Diego Maradona's daughter Giannina (Sunday Express).
In news you have heard many times before, Tottenham are set to open negotiations with Crystal Palace over a £10m deal for Wilfried Zaha (Mail on Sunday), Manchester City still want Edinson Cavani (Sunday People) and Arsenal fancy James McCarthy (Sunday Express).
So let's have a slightly different one to finish - Manchester United are monitoring Borussia Dortmund midfielder Sven Bender (Sunday Times). The 23-year-old - twin brother of Lars - has been an important part of Dortmund's double Bundesliga-winning side.