But Britain's Sun newspaper said Williams rejected "an initial approach" by Mercedes to slash in half the price of the Grove team's 2017 customer engine bill.
Williams, however, seems determined to hang onto the experienced Bottas.
"Losing Bottas would be a disaster for Williams," German language pundit Marc Surer told Speed Week.
"Williams has compromised already to finance the team by signing Lance Stroll," he said.
When contacted by the Daily Mail, Williams refused to comment on the Bottas rumours.
Another reported candidate for the Rosberg seat is Toro Rosso star Carlos Sainz, but the Spanish newspaper AS reported: "According to our sources, Red Bull is not willing to let him go."
And former team boss Gian Carlo Minardi told his website: "Despite the denial of his manager, I still see Fernando Alonso in pole position."