Somerset and Northamptonshire yesterday served formal notice on Derbyshire of their intention to engage the England fast-bowler in contract negotiations.
Malcolm, out of contract since the end of last season, has been offered a new three-year agreement believed to be worth about £40,000-a-season to remain at Derby.
After meeting the player yesterday Victor Brownett, Derbyshire's chairman, said: ``Devon has asked for more time to make up his mind. We originally imposed a deadline of the end of October for a decision, and there is no specific sticking point that I am aware of. I am doing everything possible to persuade him to stay.''
Worcestershire, Nottinghamshire, Leicestershire and Hampshire are other counties believed to be interested. The best offer is rumoured to be around £70,000-a-season.
Malcolm may be reluctant to court accusations of ingratitude at the end of a testimonial season likely to yield at least £200,000.
Leicester have confirmed they want Chris Lewis, the England all-rounder out of contract at Surrey, to return.
Glamorgan, the champions, have signed the Worcestershire reserve wicketkeeper Ismail Dawood, 21, on a two-year contract.