The Dons are understood to have submitted a bid of £500,000 for the 26-year-old, who has scored 41 goals in 99 appearances for Donny.
Derek McInnes is keen on bolstering his attacking options, and the Pittodrie side were one of a handful of clubs linked with Kenny Miller following his departure from Rangers.
Rovers are believed to have rejected a bid of £750,000 for Marquis from Peterborough United.
The English League One side are braced for further bids for the striker, who is under contract at the Keepmoat Stadium until 2020.
Marquis found the net 26 times in his first season with Doncaster as the Lilywhites secured promotion to League One. Marquis was named League Two player of the year for his goal tally.
The former Northampton Town striker added 15 goals and notched six assists during the 2017/18 campaign as Doncaster finished 15th in League One.
Marquis has also had spells with Millwall, Staines Town, Portsmouth, Torquay, Cheltenham and Leyton Orient.