Graham scored 21 times for Swansea in his season and a half in south Wales, before making a £5.5million switch to Sunderland at the end of the last January transfer window.
But the 28-year-old found opportunities limited once Paolo Di Canio succeeded Martin O'Neill, and joined Hull on a season-long loan in the summer.
Graham has been a regular for the Tigers under Steve Bruce, but he has yet to find the net.
In fact, Graham's last goal came on January 9 when he scored Swansea's second in their 2-0 Capital One Cup semi-final first leg win over Chelsea at Stamford Bridge.
Monday's clash will mark Graham's first return to the Liberty Stadium and midfielder Britton is looking forward to seeing his former colleague.
"It will be great to see Danny again. Things probably haven't worked out on a personal level for him as well as he'd liked in the last year," said Britton.
"But he was a great lad and he did fantastically well for us in that first year in the Premier League.
"He was a big character as well. Everyone will be delighted to see him and I'm sure the fans will give him a good welcome back. Twelve goals for a promoted team in the Premier League is a fantastic achievement.
"Those goals played a massive part in us staying in the division.
"We're thankful for everything he did and I was gutted as a team-mate to lose him.
"But that happens in football. We'll still have to watch out for him even though I know he hasn't scored.
"I want to see my old mates do well, but when you come up against them then you don't want them to do so well. Hopefully he doesn't score on Monday and then he scores in the next game."
The Hull game comes at the start of a week when Swansea can also reach the knockout stages of the Europa League.
Swansea will go through if they avoid defeat to St Gallen in Switzerland, although they may advance even if they lose as Kuban Krasnodar need to beat Valencia in Spain and overturn a goal difference deficit of three.
But Britton wants Swansea to go through in style.
"We haven't qualified yet, but if we were to achieve it then it would be another chapter in the club's history. We seem to keep rewriting it as we go along at the moment.
"We want to do the job ourselves. We don't want to rely on other results.
"We don't want to go through on a bit of a low by say losing the game. We want to carry on our good form from beating Newcastle and continue the winning mentality.
"It would be good to go through on the back of a win rather than a defeat."