Earlier this month, The Daily Mail reported that Tottenham are interested in signing Deeney from Watford in the summer transfer window.
Promoted side West Bromwich Albion are also reported to be looking into the possibility of signing the 32-year-old striker this summer.
The Daily Mail has now reported that should a good offer come in, then Watford, who were relegated from the Premier League last season, will not stand in the way of Deeney and will let him leave.