Should the transfer be finalised it would not, of course, be the first time that these two clubs have traded a player.
Below, Sports Mole has picked out five other footballers that have switched from West London to Manchester or vice-versa.
© Getty Images1. Ray Wilkins (Chelsea to Man United, 1979)
The midfielder rose through the ranks at Stamford Bridge and at the age of 18 was installed as the club captain in 1975 following the team's relegation to the Second Division. Nicknamed Butch, Wilkins went on to play a key role as the Blues returned to the top flight two years later. However, Chelsea's financial problems saw him sold to United for a reported £800,000 in 1979. His best moment in a red shirt came in 1983, when he scored during that year's FA Cup final against Brighton & Hove Albion. The first match ended in a 2-2 draw, but United won the replay 4-0. He was sold 12 months later to Italian side AC Milan.
© Getty Images2. Mark Hughes (Man United to Chelsea, 1995)
It came as a big shock when Sir Alex Ferguson sanctioned Hughes's departure to Chelsea in the summer of 1995, particularly because the Welshman had played such a key role in United winning the league title in 1993, before going on to star as they secured a Premier League and FA Cup double in 1994. However, it was believed that Hughes was eager for the move due to the fact that he did not want to play second fiddle to Eric Cantona and Andy Cole. He cost the Londoners £1m and would go on to play a part as the club won the FA Cup, League Cup and Cup Winners' Cup in the next three years. He departed for Southampton in 1998.
© Getty Images3. Mark Bosnich (Man United to Chelsea, 2001)
Ferguson did not hold back on his thoughts regarding Bosnich's attitude and application during his second stint at United. He was signed in 1999 to replace Peter Schmeichel, but injuries and fitness problems resulted in the United boss recruiting Fabien Barthez soon after. As a result, he was granted a free transfer to Chelsea in January 2001. However, the Australian made just seven appearances before it was announced that he had tested positive for cocaine in September 2002. What followed was a nine-month suspension from football, which prompted Chelsea to sack the goalkeeper.
© Getty Images4. Juan Sebastian Veron (Man United to Chelsea, 2003)
When the Argentine arrived at Old Trafford from Lazio for £28.1m, it was a real signal of intent from United. After all, he was regarded to be one of the best midfielders in world football at the time. He struggled to cope with the pace of the English game, although he did impress during Champions League outings. Even so, Chelsea, who had just been taken over by Roman Abramovich, were convinced to part with £15m for services and Veron went on to score on his debut against Liverpool. After that it was downhill and following two loan spells with Inter Milan and Estudiantes, he signed for the latter permanently in 2007.
© Getty Images5. John Obi Mikel (Man United to Chelsea, 2006)
Chelsea paid £12m to United for the Nigerian midfielder, despite the fact that he never actually kicked a ball for the Red Devils. In what was a confusing process, United confirmed in 2005 that they had agreed a deal with Mikel's Norwegian employers Lyn Oslo for his services. However, soon after the player and his agent claimed that they had been duped and the player had wanted to join Chelsea instead. Following the involvement of FIFA, the situation was resolved in Chelsea's favour, although the Blues did have to shell out a total of £16m to United and Lyn. Mikel remains a Chelsea player to this day.