The Sun says Newcastle have put Anderson on a £30,000-a-week deal.
Toon are eager to keep the 19-year-old Scotland Under-21 ace so have paid out first-team cash.
Anderson excelled on loan at Bristol Rovers during the second half of last season.
The midfielder struck eight goals in 21 outings for Joey Barton's side, playing an integral role in their dramatic promotion.
Rovers won 7-0 on the final day to snatch the third and final automatic promotion place - with Anderson grabbing a goal and two assists.
Upon his return, boss Eddie Howe has set about integrating him into the first team at St James' Park.