Sinclair made his move to City towards the end of the summer transfer window after informing Swansea chairman Huw Jenkins he had no desire to negotiate a new contract at the Liberty Stadium.
The winger was booed by the Swans fans when he made his final appearance for the club in the opening day win over QPR, but Routledge says the club's players understood his decision as they prepare to face their former team-mate for the first time.
Routledge said: "People get on well here and we all wish each other the best. Scott had a chance to go and joining the champions and he took that opportunity.
"I haven't spoken to Scott for a little while because he's had a lot to do up there, he's moving, but I'm sure we'll catch up on Saturday."
Routledge has benefited from Sinclair's move, taking the chance to cement a place in the first-team to become a key figure in Michael Laudrup's side, scoring two goals and creating several others so far this term.
The 27-year-old has had a nomadic career taking in spells at Crystal Palace, Tottenham, Portsmouth, Fulham, Aston Villa, Cardiff, QPR and Newcastle, but is flourishing in south Wales.
And he admits the Dane's faith in him has given his confidence a real boost.
He said: "For me, on a personal note, it's going well, I'm playing games, making chances and scoring goals so I can't ask for much more.
"People can ask you to pinpoint what it is, but I'm not sure. I'm playing more and that's probably given me a bit more confidence and now you're seeing the best of me.
"It's definitely up there (with the best form of my career), I'm enjoying my football every time I step out on the pitch and every time we train.
"That's a nice feeling because that's when you get the best out of players.
"I just want to keep playing well, keep making chances and maybe keep scoring more goals."
Swansea head to the Etihad Stadium on the back of last weekend's morale-boosting win over Wigan, but will face a City side desperate to respond after their Champions League defeat to Ajax in midfield.
However, Routledge believes the Dutch team's 3-1 victory shows there is nothing to fear for the visitors going into a game few expect them to get a positive result from, although he is under no illusion about the size of the challenge facing the Swans.
He said: "The Etihad has become something of a fortress for them there, but we've got to go there in a positive frame of mind.
"As footballers, they're in the higher echelons but sometimes you have games when it doesn't click.
"That seems to be what happened the other night, it wasn't the usual Manchester City.
"But when you play Manchester City whatever they do it's going to be a really hard game on Saturday. We have to get our minds right and be ready from the start."