Villa have already brought in Kortney Hause, Matt Targett and Tyrone Mings to bolster their defensive options, and Smith may now decide to firm up their surprise interest in Hegazi with a concrete offer.
Villa have wrapped up the deal that will see Mings return after his successful loan spell last season, with confirmation of the club record transfer expected later on Monday.
The 26-year-old wrote on his account: "Absolutely delighted to be back as a permanent @AVFCOfficial player".
"We're really pleased to have Tyrone back at Aston Villa on a permanent basis", Villa manager Dean Smith said in a statement. He helped propel Villa from mid-table obscurity to the playoff places, and helped steer the club past Derby County in the final to earn their place in the Premier League.
Mings, who made 10 Premier League starts for Bournemouth after joining from Ipswich for £8m in 2015, was keen to join the club.
He was later struck down by a spine injury which kept him out of action for a further eight months, so in all he only made 17 appearances for Bournemouth in the top flight, before his loan move to Villa last January. The Guardian report on that deal also mentions Bristol City defender Adam Webster.