The 25-year-old has been in superb form this season for Sevilla, scoring seven times in 13 La Liga appearances, while also helping Croatia claim a spot at the World Cup next summer.
According to Jutarnji List, both Manchester United and Chelsea have made it clear to the player's representatives they they would be interested in holding talks regarding a move, either in January or over the summer.
According to the Croatian newspaper Manchester United boss David Moyes is particularly keen on taking the former Schalke star to Old Trafford in order to bolster his midfield ranks.
However the Red Devils boss is unlikely to have a clear run at the midfielder with Chelsea also lurking.
Jutarnji List report that Chelsea boss Jose Mourinho was impressed with Rakitic during his time in Spain at the Bernabeu, and is now keen on taking him to Stamford Bridge.
While Sevilla have been willing sellers in the past having let the likes of Alvaro Negredo and Jesus Navas join Manchester City, they would prefer to keep hold of Rakitic, and are in talks to extend his contract beyond it's current expiry date in 2015.