Ipswich Town, Nottingham Forest and Huddersfield Town are all thought to be keen on signing the Wales international.
The three clubs are all thought to have made an enquiry to Reading about signing Church on a season-long loan deal.
Church struggled to hold down a regular place in the Reading team last season and the summer arrival of Pavel Pogrebnyak could see Church pushed further down the pecking order.
The highly-rated forward could be tempted to leave Reading this summer in search of regular first-team football and Reading could consider loaning him out so that he can get some action under his belt.
The 23-year-old, who made 19 starts in the Championship last season, netted seven goals last term to help Reading win promotion to the Premier League.