Rodgers has consistently stated that Celtic will not sell Dembele this month and the club will likely be emboldened by the fact that Virgil van Dijk is being touted for a £50million move 18 months after leaving Parkhead for Southampton in a £13million deal.
Dembele has scored 19 goals in 36 games since arriving from Fulham in a four-year deal in the summer for a development fee of about £500,000. The 20-year-old further cemented his hero status among the club's support by netting his fifth goal against Rangers in Celtic's 2-1 victory at Ibrox on Saturday.
Dembele has also shown his potential to a wider audience outside of Scotland this season, hitting a spectacular double for France Under-21s against England and scoring three times in the Champions League group stages.
But an article on the Hammers' official website stated that "a bid of £20m - a figure close to the club's all-time transfer record - was submitted for a player from Scotland", however, a Celtic Park source said they had received no official bid for Dembele.
Hammers manager Slaven Bilic earlier refused to comment on reports that Dembele was one of his main January targets.
Meanwhile Rodgers is keen to add to his squad ahead of another European campaign and Celtic are working on finalising a £2.8million move for 19-year-old Ivorian midfielder Kouassi Eboue from FC Krasnodar.