Midfielder Joe Allen is a player Moyes wanted to sign for West Ham before he left 18 months ago, while goalkeeper Darren Randolph has been lined up for a possible return.
West Ham are also in the market for a new forward and have been offered Gabriel Barbosa, who has been on loan at Flamengo from Inter Milan.
Barbosa, who is nicknamed ‘Gabigol’, is thought to be available for around £16million and Moyes confirmed he has money to spend, saying: “I think there is money there to spend if we need it.”
Moyes has stressed that his main concern is getting the best out of the players already at West Ham, including England midfielder Declan Rice.
Rice had been struggling to reproduce his best form over recent weeks, but put in an excellent display in the first game of the new Moyes era, a 4-0 thrashing of Bournemouth.
The 20-year-old revealed that he received the hairdryer treatment from Moyes during his last spell at the club and is expecting more of the same from the Scot this time around.
“I made a mistake at Arsenal when I ducked for the ball and missed a header, and it went in,” said Rice. “It was 1-1 at the time and I got out of the way of the ball, and afterwards he came for me in the changing room in front of the lads.