The Blues tabled an official bid for the unsettled striker earlier this week, but their overtures were rebuffed by the Old Trafford outfit.
Jose Mourinho insists Rooney is their number one transfer target and they are expected to come back with a new bid for the England international.
Schwarzer, who recently joined Chelsea on a free transfer after leaving Fulham, has welcomed the club's pursuit of Rooney, feeling he would be a valuable addition to the squad at Stamford Bridge.
"I think over the years Chelsea have shown a tremendous amount of ambition and that just continues now by bidding for one of the top players in English football," Schwarzer told Sky Sports News.
"The club always wants to continue to go forward and that is what is very exciting about being here.
"He is definitely one of the best strikers in the world without a doubt and he would be an asset to any side."
Asked if he would like to play alongside Rooney at Chelsea, Schwarzer added: "That is not my choice, but he is a phenomenal player and an asset to any side."
Cech also endorsed Chelsea's pursuit of "great player" Rooney and knows nothing can be discounted in football transfer business.
"Wayne Rooney is a great player but at the moment he's a Man United player," Cech said.
"We'll see what's going to happen. He's a great player. Let's see.
"You always want to have the biggest and strongest squad so you can challenge for titles.
"That's why you have a manager and sporting director to take care of that and you have to do the most important part and that's the work on the pitch.
"We already have a few more players and a great squad. If the manager doesn't think we have enough he will try to get players in. It is only his decision.
"For players, we concentrate on getting fit and doing our best, to play as much as we can. That's all we can do.
"In football things are changing every day with every squad. As time goes on, every team can make some changes. Anything can happen."
Mourinho, whose second spell as Blues boss began with a 1-0 win over Singha All-Stars in Bangkok on Wednesday, has already signed Andre Schurrle, Marco van Ginkel and Schwarzer, the latter providing back-up to Cech.
Cech is one of the survivors from the Special One's first spell at Stamford Bridge, when Chelsea won a first Premier League title in 50 years in 2005 before retaining the trophy as the Portuguese established himself as the most successful manager in the club's history.
Cech sees little alteration in Mourinho after nearly six years away.
"He is as hungry as ever, he wants to be successful," Cech said.
"When you have someone who works at such a high standard every day it never changes. It's the same.
"He doesn't do things just for nothing, he always wants to win games, no matter if it is a Premier League game or a pre-season game or Champions League game.
"He's always pushing the players hard to train, to concentrate, to do things in the right way."
Mourinho praised the 'old guard' earlier this week, but Cech recognises there are no favourites in the squad.
"It's the same whether you are 40, 31, 45, 28 or 15," Cech said.
"If you are good enough you play, if you are not good enough you don't play. I think everybody will play on merit, we have to earn our places and we are working to do so."