Following back-to-back defeats in the Championship and a dire start to the campaign, Nuno was let go by the West Ham board as fans chanted for him to be sacked.
Ahead of Wednesday's game at Cardiff City, West Ham sit in eighth position in the Championship table, as reports state that the Hammers are set to have a new coach in charge ahead of kick-off.
Parker, 46, made 129 appearances for West Ham as a player and has been out of work since leaving Burnley back in April.
The former midfielder has achieved promotion to the Premier League three times from the Championship with Fulham, Bournemouth and Burnley in the 2024/25 season as his side won automatic promotion.
This weekend's clash against Cardiff is followed by fixtures against Blackburn Rovers, Preston North End and Portsmouth in what is a favourable run for the club, who are still seeking promotion.
Redknapp backs Parker
Former West Ham manager Harry Redknapp told talkSPORT Breakfast that the hiring of Parker would suit the club.
“Scott's got a great record in the Championship, having taken teams up. He knows the club. He was a very, very good player. I took him from West Ham to Tottenham.
“He’s a good lad. He was a very, very good player and a very astute manager. So I think he's a great fit for West Ham. I went to the club at 14 and looking back all those years, I think this would probably be the worst group of players I've seen at West Ham in that time.
“So he hasn't got an easy job on his hands. Take (Jarrod) Bowen aside, the rest of the squad, there are very few players there that would have got in too many West Ham teams over the years.
“But they've got great support. It's a massive club that unfortunately needs a big lift now. Hopefully Scott can go in and give them that lift they need.”