They were believed to have suggested offering defender Dean Richards on loan for the season as part of the deal, but the Upton Park club are not pursuing this part of the offer.
Arsenal and Portsmouth were interested in Carrick but both deals fell through and Hammers manager Alan Pardew has reportedly told Carrick to make up his mind up about a move or sign a long-term contract.
Crystal Palace manager Iain Dowie is still keen on Carrick despite being told the player is not interested in a move to Selhurst Park. Dowie said: "We'd still like to offer Michael Premiership football. If he wants to come I'd be delighted to chat with him."
Doherty, meanwhile, has become renowned for his versatility since joining Spurs from Luton, but has failed to earn regular first-team football at White Hart Lane under a succession of managers.
Doherty can play as a central defender or in attack but prefers the former role.
Norwich have been looking to bolster their defensive strength for some time and see Doherty as a perfect addition to their squad.
Doherty almost joined Cardiff in January but the deal fell through at the last moment.
The player's fortunes then turned round following Tottenham's decision to sack Glenn Hoddle and install David Pleat as caretaker manager until the end of the season.
Pleat, who was responsible for bringing Doherty to the club, restored the player to the Spurs line-up and Doherty was ready to extend his stay with the club.
However, he has never been a favourite with the fans, who booed him during their pre-season friendly defeat against Cagliari two weeks ago.
Blackburn are giving a second trial to Nigerian striker Peter Odemwingie, one of the stars of this year's African Nations Cup.
