Championship trio Sunderland, Middlesbrough and Sheffield Wednesday are said to have already discussed signing Gyasi.
However, it is claimed that Sunderland wanted the Ghanaian on loan, while Aalesund favour a permanent deal.
The report adds the Norwegian club are willing to accept £600,000 up front for Gyasi, who is out of contract at the end of 2018, with add-ons which could take their potential earnings to more than £1 million.
That asking price is said to have 'alerted others' to the possibility of signing the 26-year-old, and Brighton, Fulham and Norwich appear to have seized the initiative - making contact with Aalesund.
Though only capped twice by Ghana, Gyasi, who scored or created 10 goals in 27 league games last season, would not require a work permit to move to English football, having been born and raised in the Netherlands.
Would Gyasi be a good signing for Brighton & Hove Albion, Fulham or Norwich City?
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