The Hammers were prepared to offer a club record £25million for the Portuguese international, but Sporting wanted a fee closer to his £39.5m release clause.
Slaven Bilic’s side sent representatives to Portugal to try and thrash out a deal for the highly-rated holding midfielder, but there is no end in sight to the impasse.
Instead, reports claim West Ham could turn to Carvalho’s compatriot Andre Gomes, who has been made available for a loan move by Barcelona.
ESPN say Barca are willing to listen to offers for the midfielder, who joined from Valencia last summer, as he does not figure in new manager Ernesto Valverde’s plans.
The 24-year-old made only 17 starts in La Liga last season and he has made only one appearance this season in the second leg of the Spanish Super Cup against Real Madrid.
Italian champions Juventus and London rival Tottenham have also reportedly shown an interest in signing Gomes, but West Ham are hoping to beat them to the chase.
Another move which is being considered is a loan move for Arsenal’s Jack Wilshere.
Wilshere spent last season on loan at Bournemouth and he could be set for another spell away from the Emirates this term.
The Sun claim West Ham are considering taking the 25-year-old on a season-long loan, but will wait to see if they can reignite a last-minute deal for Carvalho before making their move for the England midfielder.