The 19-year old Wales international has started 12 of the Hoops' 16 league games this season but there are fears he may lose his first team spot when Swedish defender Mikael Lustig joins the club in January.
Despite that speculation, Lennon is determined to keep Matthews at Parkhead as the Toffees and Cottagers continue to keep an eye on him.
"We think they are very talented players, but we are certainly in no rush to let Adam go," Lennon said.
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