The Hammers have been offered the chance to take Arnautovic back on loan and David Moyes had been open to a reunion with the Austrian forward.
Arnautovic left West Ham in acrimonious circumstances in 2019 after pushing for a lucrative move to China. He earns around £100,000 a week at Shanghai SIPG and West Ham are unwilling to cover his wages.
Moyes was able to turn the Arnautovc’s career in Stratford around during his first spell at West Ham, deploying the former Stoke City man through the middle with great success.
Arnautovc scored 11 goals and claimed six assists during 26 games under Moyes having not scored a single goal for the Hammers before the Scot arrived at the club.
Moyes has been keen to bolster his attacking options to take some of the load of talisman Michail Antonio.
The Hammers are also keen to add a left-back if the opportunity arises following Arthur Masuaku’s knee surgery, though funds are limited.