West Ham United are said to be among the teams serious about securing their signature.
Per The Sun, West Ham want to ensure they are not falling foul of homegrown rules.
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O'Hare, 25, has starred for Coventry City this season, especially in their FA Cup semi final run.
Aston Villa, Fulham and Championship side Southampton are all keen on the soon to be free agent.
Greaves is presently at Hull City, but would find a move to West Ham very appealing.