West Ham also have Spanish shot-stopper Adrian who has been the first choice keeper for the Hammers in the past and could provide competition for the spot, making them reluctant to spend too much.
According to the Sun, West Ham have had an initial bid of £4.5m rejected by the Swans as they continue to stand firm on their asking price. Fabianski is currently away with the Polish national team so any deal will almost certainly have to wait until after the tournament.
Fabianski’s Swansea teammate Alfie Mawson is also high up West Ham’s wish list and the east London side had hoped to tie up a double swoop with their initial enquiry.
The Swans are expected to demand £18m for their centre-half though and with them asking £7m for Fabianski, West Ham may now look to pursue the deals separately.
West Ham already missed out on defensive target Jonny Evans this summer so will prioritise a move for Mawson to bolster their back line. They are expected to return with a new bid for Fabianski though that will be closer to the Swans valuation.
Fabianski has been one of the top performers for Swansea over the past four seasons but he is eager to depart the Welsh coast after the Swans were relegated from the top flight last season.
The Polish keeper wants to secure a quick return to the Premier League which could play into West Ham’s favour as the summer transfer window rages on.