Edouard completed his move to Celtic earlier this month following an encouraging debut campaign on loan from Paris St Germain.
Fans are keen to see the Hoops strengthen their options in defence after January arrivals Marvin Compper and Jack Hendry failed to make an immediate impression, but while Rodgers is looking to add to his squad, he is keen to wait for the right deal.
“The key was to get the likes of Tom (Rogic, who signed a new deal) and Odsonne in,” he told CelticTV.
“Like always, there are a few areas that we want to be better in and improve.
“It’s never easy because the team we have is developing very well and I like to develop our own players.
“Everyone goes on about a new centre-half, but I don’t think they’d be happy with Billy McNeil playing centre-half!
“We have young players developing very well and they will continue to, but we have to be in the market to bring the best possible players to Celtic but there are two conditions: availability and affordability.
“We are always on the lookout.”
The deal to bring in Edouard was seen as a priority this summer following a loan spell which saw him net 11 times in all competitions, including three in two games against Rangers, particularly with Moussa Dembele continually linked with a move away.
The striker signed a four-year deal in Glasgow and Rodgers is excited to see the Frenchman continue his development.
He said: “I was delighted. Coming in on a loan deal, we knew he was a talent and he proved over not just the games, but in training every single day, (that) he is an outstanding player and has every attribute but still needs development and improvement.
“He came in as a 19-year-old, scored some important goals.
“His link-up play, his movement, everything, he is such a talented player and we think this is a great platform for him to come to a big club and prove more and develop.
“I think it is an exciting period for him.”
The Celtic players have returned to training with their new season due to get under way in a little under three weeks following the Champions League qualifying draw on Wednesday.
The Bhoys, who have been entered into the first round of qualifying this season, face Armenian side Alashkert as they begin their bid for a group-stage spot and Rodgers admits he does not know a lot about their opponents.
“I don’t know much about them,” he admitted. “But I will do before we play.
“In my experience of these games, they are always tricky ties.
“Whether it is heat or travel, you have to prepare as best you can. The first leg being away, we will have to deal with it and then we have the second leg at home.
“The objective over the two legs is to qualify and however that comes at this stage of the season, that is all we are looking to do.”