Both Manchester United and Chelsea have both been rumoured to be interested in the Croatian international, after the 25-year-old has impressed for Sevilla this season.
The centre-midfielder has scored nine goals and 12 assists in all competitions so far this season and is one of the most impressive players in La Liga this season.
David Moyes will be looking for a creative, goal-scoring midfielder this January as he missed out in the summer on the signing of Cesc Fabregas, while Mourinho will hope to add firepower to his midfield, with rumours suggesting Essien is wanting away from Stamford Bridge.
However, French giants PSG have now entered the race according to TalkSport, which will dent the Premier League clubs chances of signing the £11million rated midfielder if PSG do put in a bid.
The huge financial backing at PSG could allow Laurent Blanc to brush aside both United and Chelsea with the contract offer for Rakitic.
With a year and a half left on his contract, Rakitic would be an ideal signing for Moyes this January, as a player who can control the midfield and get a few goals for the club.
Mourinho doesn't necessarily need another centre midfielder, however the Portuguese manager could see Ivan Rakitic as the perfect replacement for the ageing Frank Lampard.