The 24-year-old, currently with Real Oviedo, has been a long-standing target for the Scottish champions.
His performances at the World Cup for Egypt had the potential to increase his market value and attract interest from other clubs.
Celtic had previously been rumoured to have made a £3.4 million bid for Hassan, which was rejected by Oviedo.
The Spanish club had reportedly set a £10 million release clause in his contract, a reduction from £14 million following their relegation.
However, Spanish outlet lne.es claims that a move to Celtic is now close for the winger.
The report suggests that Glasgow was always Hassan’s most likely destination, and negotiations have been progressing well, with final details still to be thrashed out.
In a recent statement, Hassan hinted at the possibility of leaving Oviedo, saying: “I haven’t spoken to anyone at Oviedo yet, but I have one year left on my contract and nobody is untouchable at a club like this.
“Football is a business and, at my age, I think I can bring in some money for the club.
“But I don’t know what will happen.
“I’m very happy in Oviedo. They’ve always treated me well and I’ve experienced the best time of my career here.
“Oviedo will always be a part of my heart, but we’ll see what happens.
“I don’t know if I’ll stay or not.”
