Sheaf played a key role in Coventry's run to the FA Cup semifinal this season.
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The Sky Blues are seeking 10m to sell.
Both the Cottagers and Ipswich are keen on Sheaf, who rejected Luton in January.
Fulham, Ipswich target Coventry midfielder Ben Sheaf
The former Arsenal junior is also wanted by Premier League new boys Ipswich Town, says The Sun.