Ibrox boss Walter Smith is a big fan of the combative midfielder and could make a swoop after Wigan slapped a £2.5million price tag on Wigan's Lee McCulloch, according to the Sunday Mail.
It is claimed the Hammers would let Quashie, who almost joined the 'Gers when Alex McLeish was manager, leave for a fee of around £1.5million.
The midfielder's proposed loan move to Ibrox in January 2006 fell through due to speculation over the future of McLeish, who left the club just four months later.
At the time Quashie said: "There was constant talk of Alex leaving. If I went there and he left a few weeks later that would have put me in a difficult position.
"David Murray and Alex were brilliant with me but it was a complex situation."
Quashie was called up for Scotland by former boss Berti Vogts despite winning England Under-21 honours and has played 14 times, with eight of his caps coming during Smith's spell in charge of the national team.