The 22-year-old has made just under 100 appearances for Sampdoria since joining the club from Atletico Madrid as a youth player in 2008.
Over the last few weeks, West Ham have made repeated contact with the Genoa-based outfit to try and come to an agreement over a transfer, but so far they have had little success.
The two sides had a good chance to chat over the weekend when they faced off in a pre-season friendly, which West Ham won 3-2.
The latest reports from Italian newspaper Tuttosport suggest that Sampdoria sporting director Carlo Osti doesn't want Obiang to leave and won't do anything to make the Hammers' job in luring him easier.
Despite Obiang's disappointing 2013-14 campaign, Osti has reportedly told West Ham that he won't accept anything less than £4.8 million.
That sum may have been calculated to put the Premier League side off because it is above the general market valuation of the player.
West Ham are expected to respond to Sampdoria within the next few days, but it looks like there is no room for negotiation.
It is believed that Obiang would be in favour of a move in principle due to the allure of English football and the chance for a fresh challenge, but the talks may never get as far as personal terms.