The Mirror says Parker said after the win at Bournemouth that he wants both Serbian striker Mitrovic and midfielder Cairney to stay in order to build a squad to get out of the Championship next season.
The Cottagers may now offer both new deals in order to try to persuade each to stay. But Mitrovic, valued at £30m by the club and only signed last summer, has already had offers from China, and West Ham and Crystal Palace are both interested.
Parker's chances of landing the manager's job full time in the summer have been boosted by the wins over Everton and Bournemouth – but the club have also looked at Celtic manager Neil Lennon as a possible appointment.
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