Battling midfielder Khedira has been heavily linked with both London clubs over recent months with his current contract at the Santiago Bernabeu due to expire next summer and negotiations over a potential extension having seemingly ground to a halt.
Manchester United plan bid
Faced with the risk of losing him on a free transfer at the end of the season, speculation has been rife that Real could offload the 27-year-old at a reduced price in January and, as such, Goal now report that Manchester United are plotting a winter offer in the region of £10 million for his signature and are even willing to meet his extravagant £200,000-per-week wage demands.
Intriguingly, the same source suggests that the decision to pursue Khedira comes as a result of the club searching for a cheaper alternative to Dutch international Kevin Strootman - a known favourite of Louis van Gaal who is not expected to be sold by Serie A outfit Roma in the upcoming window for anything under £30 million.
2014 has been a very mixed year indeed so far for Khedira. After missing the majority of last season with a severe knee injury sustained during an international friendly against Italy, he did manage to return in time for Real's Champions League final victory over rivals Atletico and also made five appearances for Germany as they romped to World Cup success in Brazil.
A memorable month in South America does not seem to have improved his domestic situation, however, with Khedira falling down Carlo Ancelotti's pecking order in Madrid thanks in part to his reluctance to pen a new deal and also as a result of Real's slightly unnecessary double acquisition of compatriot Toni Kroos and James Rodriguez .
Indeed, Khedira - who first moved to the Spanish capital from Stuttgart back in 2010 - has made just two substitute appearances in La Liga so far this season and is currently sidelined after undergoing knee surgery earlier this month.
Khedira over Strootman?
Manchester United significantly upgraded their midfield during the recent transfer window after years of failing to address the position properly, with Daley Blind and Ander Herrera moving to Old Trafford along with Khedira's former club teammate Angel di Maria.
Despite these arrivals, however, it could certainly be argued that manager Louis van Gaal still lacks a real box-to-box presence with a proven track record at the highest level.
Given his connections with Van Gaal, Strootman seems to be the popular choice. However, with the Roma man yet to return from his own devastating anterior cruciate ligament injury, it could certainly be deemed as a sizeable risk to pay a significant price for his services unless he has fully demonstrated that he has fully recovered from such a blow.
Khedira's own patchy record in this regard should also be a concern, although a £10 million fee is barely a drop in the ocean for a club of Manchester United's stature so the risk would not appear be too high financially.