The Everton centre-back has been heavily linked with a switch to Stamford Bridge this summer and reports in the media on Friday suggested he was ready to force through a move by handing in a transfer request.
The Blues have already seen two bids for the 21-year-old rejected by the Toffees, but are hopeful of agreeing a deal before the transfer window closes next month as manager Jose Mourinho has reportedly identified Stones as a potential long-term replacement for captain John Terry.
However Keown, who made over 100 appearances for the Merseyside outfit during his playing days, says Stones should continue his development at Goodison Park for at least another season:
“He should stay. He still needs to grow as a player and he needs to know he is number one choice,” he told talkSPORT.
“I don’t think the [Chelsea] manager is completely stable at the moment, he is going through a really difficult period, and he is better staying at Everton for another season.”
“They adore him, the Evertonians. They got me in the England team because they were so supportive. He needs that warmth for at least another year for his development,” Keown added.
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Stones has been a revelation since his arrival at the club from Barnsley in the 2013 January transfer window and has a good chance of being included in the England squad for next summer’s European Championships.