Mercedes have had one offer for 27-year-old Bottas turned down as they search for a replacement for Rosberg.
Rosberg, 31, shocked the sport when he decided to retire just five days after being crowned champion and it remains to be seen who will fill the German's boots to team up with Lewis Hamilton for 2017.
Earlier on Tuesday, Mercedes non-executive chairman Niki Lauda insisted his team were yet to make a decision on Rosberg's replacement and said they may wait until the end of January before making an announcement.
Meanwhile, Williams have announced chief technical officer Pat Symonds will step down from his role - with rumours persisting that Paddy Lowe of Mercedes is set to fill the void.
Symonds has been with the British team since 2013 but is now leaving at the end of the year.
The 63-year-old, who had a storied history in F1, arrived at Williams from Virgin Racing in the middle of the 2013 season, helping the team to third in the constructors' championship in his first full year.
Lowe, the technical executive director of reigning champions Mercedes, is widely reported to be close to a switch to a senior technical role at Williams.