Widdecombe has seen a surge in popularity following her appearance on the BBC One show Strictly Come Dancing this year, and the BBC reportedly wishes to capitalise on this.
"I would truly love to present Songs of Praise and hope it will happen," Widdecombe told The Mirror about the rumours. "I think the show is just fantastic."
"Aled [Jones] is a fantastic host and the last thing I want to do is replace him," Widdecombe clarified. "I would not mind sharing the spot with him."
The BBC has yet to make any official announcement regarding the rumours.