West Ham have agreed deals in principle to sign Harry Maguire and James Ward-Prowse, the PA news agency understands.
Manchester United defender Maguire and Southampton midfielder Ward-Prowse have also agreed personal terms with the Hammers.
Maguire remains in discussions with United about the terms of his exit from Old Trafford but the transfer, understood to be worth around £30million (34 million), is expected to go through.
The Hammers are also close to announcing the £35million signing of Mexico midfielder Edson Alvarez from Ajax.
The 25-year-old has passed a medical, but the paperwork is still being completed.
Meanwhile, West Ham are understood to have knocked back an initial £60million approach from Manchester City for midfielder Lucas Paqueta.
That figure is some £30million less than West Ham would entertain selling the Brazil midfielder for.
However, there could be a player swap involved with Hammers boss David Moyes having long held an interest in City midfielder Kalvin Phillips.
Alvarez and Phillips can both fill the position vacated by the £105million sale of Declan Rice to Arsenal.
Young winger Cole Palmer, who scored in Sunday’s Community Shield defeat by the Gunners, is another player admired by Moyes.