Eriksson has been heavily linked with the forward, whose club Toulouse have already rejected a £7million bid from French champions Lyon.
Given City's chronic lack of goals last term - just 29 in the Premier League - Eriksson has made bolstering his attacking ranks a priority now he has been installed as Blues boss.
The former England chief knows it would take a bid in excess of £8million to lure Elmander to Eastlands, but with new owner Thaksin Shinawatra pledging to back Eriksson to the hilt, those funds should be easy to acquire.
However, while admitting his admiration of his fellow countryman, who has 27 caps and was part of Sweden's 2006 World Cup squad, Eriksson is refusing to get carried away by the prospect of signing him.
"Elmander is a very good striker," Eriksson told the Manchester Evening News.
"He has had a tremendous development during the last two years and is a proven international.
"He is a very interesting player but that does not mean he will play for the Blues next season."
With less than five weeks to his opening game in charge at West Ham, Eriksson knows he needs to act fast if he is to strengthen a squad which has already lost key duo Joey Barton and Sylvain Distin during the summer.
A formal pre-season programme, beginning with a trip to Doncaster on Saturday and ending with the annual Thomas Cook Trophy - against top-class Italian opposition - on August 4, is expected to be announced on Monday.
Eriksson could also confirm his choice as assistant following the failure of talks with current Sweden number two Roland Andersson.
Former Manchester United star David Platt has been linked with the job in some quarters, although a more likely candidate is Hans Backe, whose last major job was as coach of Panathinaikos.
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