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," he 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."