West Ham are preparing to replace captain Declan Rice this summer.
Manchester City midfielder Kalvin Phillips and Chelsea's Conor Gallagher are being considered by the Irons.
The Hammers have been long-term admirers of the England duo and their situations are being monitored, says the London Evening Standard.
No formal approaches have been made, though the camps of both players are aware of West Ham's interest.
Rice is expected to leave this summer after resisting new contract talks, his current deal has just over a year to run.