Sunderland assistant manager Paul Bracewell is understood to have watched the 21-year-old in action for Town against Ipswich last week.
Sunderland’s January transfer business will be very limited given the constraints of the £140million debt and the Premier League financial fair play restrictions around wages.
Wage restrictions mean Sunderland can’t even make a loan signing unless wages are freed up by selling players.
But manager David Moyes has identified adding a centre-back and central midfielder to his squad if wages can be freed up.
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Injury-hit Sunderland will also be without Lamine Kone in January when he teams up with Ivory Coast for the Africa Cup of Nations.
Webster could be a viable option to add to the squad and Ipswich Town manager Mick McCarthy has said previously that Webster has the potential to play in the Premier League.
Speaking back in September, McCarthy said: "He’ll play in the Premier League – whether that’s with us or with someone else.
"People will be watching him, there’s no doubt about that.
"He’s quick, he’s very comfortable with the ball, he can break forward with the ball and he’s got two good feet.
"What I like about him more than anything though is he’s bought into our defensive side of the game. He’s got better and better. I’m really pleased with him."
Webster has made 18 appearances so far this season, scoring one goal in the defeat to Birmingham City last week.
The 21-year-old centre-back was signed from League Two side Portsmouth for a fee of £700,000 – the most McCarthy has spent on a player during his spell in charge at Portman Road.