The towering Egyptian defender will be allowed to leave the Baggies this summer if another club stumps up double figures for the 27-year-old.
West Ham are believed to be eyeing up his release clause, as are a number of other Premier League sides.
Losing Hegazi would leave Albion desperately short at centre-back after Jonny Evans joined Leicester for £3.5m due to his own release clause and long-serving defender Gareth McAuley was released last week.
It would leave Craig Dawson as the only recognised centre-back at the club with a first-team appearance for the Baggies, although promising 20-year-old Jack Fitzwater recently signed a two-year contract.
However, receiving £10m for Hegazi would represent a significant profit six months after Albion paid Egyptian club Al Ahly £4.5m for his services and handed him a contract until the summer of 2022.
Hegazi was spotted playing for Egypt in the 2017 African Cup of Nations by former boss Tony Pulis and joined on loan last summer before his move was made permanent a week before Christmas.
He started all 38 Premier League games last season and completed more minutes in an Albion shirt than any other player in the squad.
Hegazi is returning home from Russia this week after Egypt’s World Cup ended in a 2-1 defeat to Saudi Arabia.
He is not the only Albion player who could be snapped up this summer due to a release clause.
Nacer Chadli has a £17m release clause in his contract and Salomon Rondon can leave for £16.5m.
Hegazi’s release clause further strengthens Albion’s stance over Dawson, who is wanted by Burnley.
West Ham had a £12m bid for Dawson rejected a fortnight ago and have not returned with another offer, having instead turned their attentions to Hegazi.
But Burnley are keen on both Dawson and Jay Rodriguez, and had a £25m bid for the pair rejected.
Albion want north of £20m for Dawson, and will not budge on their valuation because losing him could leave their whole backline needing major surgery.