Sinclair joined Manchester City after refusing to sign a new deal at the Liberty Stadium and was then booed in his last game for the club, away to QPR on the opening day of the season.
Routledge says the club's players understood Sinclair's decision to join the champions and are looking forward to catching up with the 23-year-old on Saturday.
He told Sky Sports News: "People get on well here and we all wish each other the best. Scott had a chance to go and join 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."
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Sinclair's departure actually benefited Routledge, allowing him to cement a place in Michael Laudrup's starting line-up.
The 27-year-old has had a nomadic career, including spells at Tottenham, Aston Villa, QPR and Newcastle among others, but believes he has finally settled at the Welsh outfit.
"For me, on a personal note, it's going well," he continued. "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."