Allen had been widely tipped to leave Stoke this summer following their relegation from the Premier League.
West Ham United were linked with the Wales international in January, while Newcastle United are believed to be admirers of the 28-year-old.
However, according to The Telegraph, Allen is in 'advanced talks' with Stoke over a new contract.
The midfielder had been in line for a 50% wage cut following Stoke's relegation, but the report claims that new terms have been offered to convince the Welshman to stay with the Potters for their 2018-19 Championship campaign.
Allen scored four times and registered seven assists in 38 appearances for Stoke last season.