The 28-year-old attacker has contributed six goals and four assists in eight appearances for the Hammers since arriving on loan from Manchester United in January.
The pair have struggled to make an impact at Old Trafford this season and could allegedly be moved on by Ole Gunnar Solskjær this summer.
According to The Independent, West Ham boss David Moyes is keen to reunite with Jones and Lingard at London Stadium, having worked with them during his stint as Man United coach.
Chelsea boss Antonio Conte is reportedly lining up a move for Manchester United midfielder Jesse Lingard in the summer, according to The Sun.
Conte is keen to sign the 23-year-old playmaker to fit into the Blues’ system as the Italian manager looks to strengthen his squad ahead of their return to the Champions League.