The 27-year-old has been a key player for Mark Hughes ever since he joined the Potters from Liverpool.
Moyes to add more composure and versatility to his midfield and Allen would be a cracking addition to his side. The Stoke City star can control the game from the deep and he can play an advanced role as well. According to Mirror, Allen is a key target for David Moyes in January. Allen has the technical ability to control the tempo of the game and dominate the lesser sides with ease.
The Hammers have improved since the arrival of Moyes but it is clear that they need new signings in order to finish in the top half this season.
As per the report, Moyes is eyeing up moves for Alfie Mawson and Lamine Kone as well.
It seems that the West Ham boss is looking to strengthen his midfield, defence as well as the attack. The Hammers have been linked with a move for Daniel Sturridge.