The Royals are preparing for life in the third tier after dropping out of the Championship and need to regroup and rebuild.
Wilder is in the frame to take charge, with his experience rebuilding Sheffield United and Northampton counting in his favour.
The experienced boss took over at Watford on a short-term deal in March and is poised to depart Vicarage Road when it ends.
He wants to quickly return to management and Reading may fit the bill.
It is unclear what level of budget Wilder would have to work with if he takes the Royals job.
His stock has dipped since his exit from Sheffield United though, with mixed results from his time at Middlesbrough and Watford.
He won promotion from League Two while in charge at Northampton and led Sheffield United out of both League One and the Championship.
