Hayden has enjoyed a successful two years at St James' Park, with with a total of 67 appearances being made in all competitions.
However, according to The Mirror, the 23-year-old is trying to secure a move away from the Magpies in order to return to the South of England, where he began his career with Arsenal.
The report claims that Newcastle are against parting ways with the Englishman before the end of the month, but both Villa and Stoke are looking to tempt the Magpies into a deal.
Both clubs are looking to make additions ahead of a bid to secure promotion from the Championship, and Hayden has previously played a role in helping Hull City and Newcastle earn a place in the top tier.
Hayden still has three years remaining on his contract.