The Spanish giants have told the Hammers that they are willing to sell Vermaelen, but only if they receive a bid of over £10 million.
They have also told West Ham that they do not have much time to think over whether they want the former Arsenal man.
Barcelona want to push through a deal for Vermaelen, if they are to sell him, with West Ham having just days to persuade the centre-back to join.
West Ham are on the look out for a new centre-back following the exit of James Tomkins to Crystal Palace.
The Hammers are currently short of numbers in defence, but Slaven Bilic believes that Vermaelen would improve his options.
Vermaelen has struggled to make an impact at Barcelona since moving there back in 2014.
West Ham have already made five signings so far this summer, following the additions of Gokhan Tore, Sofiane Feghouli, Toni Martinez, Havard Nordtveit and Domingos Quina.