Routledge suffered an ill-fated spell with the Magpies before joining Swansea, playing just 36 times in two seasons at the club.
However, the 27-year-old has made a fine start to the season for the Swans, and Graham believes that the winger can continue his good form on Saturday and show Newcastle that they did not see the best of him.
"Wayne has been superb - he is probably in the best form of his career. He was always a tricky winger who could get assists and do well for the strikers, but he's added goals this season which has made him a real threat for us. Now he's going back up there [to Newcastle]," said Graham.
"I always joke to Wayne that he's lived my dream playing for Newcastle. We live in the same apartment block and always have a bit of banter about it. I'm sure he wants to go back and prove a point for himself. Newcastle wanted rid of him and he's had a superb season, so it's up to him to show them what they're missing out on.
"He's a top bloke, a down-to-earth guy. He's had his highs and lows. He had his great move to Tottenham from Palace and had to deal with not playing there. It's been tough for him. He's been on loan everywhere and it's hard to be in and out of teams. You need to be settled and enjoying your football, and I think that's what he's doing this year."
Swansea currently sit 11th in the league table, one place and one point behind Saturday's opponents.