The Championship club are seeking to bolster their squad ahead of their quest to bounce back to the Premier League at the first time of asking, and have identified the Scotland international as the player to help them do so.
According to Chronicle Live, the Potters are attempting to lure Ritchie to the club with a lucrative wage packet worth £75,000-per-week plus bonuses while simultaneously tabling offers to the Magpies in the hope of forcing their hand.
However, the report claims the official £15m offer from Stoke has been met with disdain, with manager Rafa Benitez unwilling to part with the 28-year-old unless he receives a suitable replacement in turn.
Ritchie is said to be open to staying at St James' Park but should his time at the club be forced to come to an end then his preference would be to return to the south coast rather than link up with Stoke.
Middlesbrough have been linked with a move for Ritchie this summer alongside former club Bournemouth.
The Magpies' firm stance in the transfer market has arisen in part due to the soaring cost of a number of their transfer targets, which include Chelsea's Kenedy and Crystal Palace's Andros Townsend.
Ritchie has spent two seasons with Newcastle, scoring 19 goals and setting up 16 more across 86 appearances for the Premier League outfit.