Salomon Kalou and John Obi Mikel are set to remain with Chelsea.
The London Evening Standard says the duo were understood to have grown unsettled under Carlo Ancelotti as they struggled to secure a regular starting role in the second half of the campaign.
Both players were believed to be considering their futures at Stamford Bridge, while there was increased speculation that the club might sell them anyway.
Kalou was particularly disappointed at his treatment having hit a personal best of 13 goals this term, yet he still started only 22 matches.
Ancelotti has already paid the price for a disappointing season by being fired on Sunday, but the club are due to make a number of changes to the squad this summer.
However, Chelsea want to keep Kalou and Mikel, who are 25 and 24 respectively, because their priority is to get rid of some of the older members of the squad and keep what young players they have in the ranks.
