The Colombian international is ready to leave the club in search of first-team action as it was reported in June that he had agreed personal terms with United ahead of an impending summer move to Old Trafford.
However, a deal between the two clubs is yet to be agreed as Madrid are still holding out for a massive €75m (£66.4m, $85.5m) fee.
Meanwhile, Premier League champions Chelsea have also shown interest in the 2014 World Cup star, according to Spanish publication AS.
With the expected sale of Diego Costa to Atletico Madrid, the Blues will have the funds to lure Rodriguez as they look for reinforcements ahead of their title defence, especially with star man Eden Hazard set to miss the start of the 2017/18 season through injury.
Paris Saint-Germain are another club interested in Rodriguez, who only started a measly 13 league games last season for the Champions League winners.
However, Modric, who played for Tottenham before he joined the Spanish capital in 2012, has issued a warning that leaving Madrid for any other club would be a step down.
"You're at the best club in the world, that's for sure, and from there you can only go down.
"Everyone will have their reasons. If I continue like this, I will do everything possible to stay, but things in football change fast."
While it is true that not many clubs are a better prospect than Los Blancos, first-team action is something that only a few players at Madrid are guaranteed of and in this case, a move away would be ideal for Rodriguez.