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In the wake of striker Steffen Iversen's new deal which keeps him at the Lane until 2006 - announced on Thursday - the club are determined to reward Carr for his continued improvement.
Pleat said: "I have sat and spoken with Stephen's agent. They were quiet talks, pleasant talks and private talks and that's where we are now.
"We will obviously be looking to do something for Stephen, not necessarily immediately, but we will do something. He has an existing contract and Spurs fans have nothing to fear."
One of the most consistent players at Spurs for years and last season's Player of the Year, Carr is now seen as one of the best full-backs in the Premiership. The Irish international has picked up where he left off last season - scoring and creating a goal against Ipswich Town on the opening day and seeing an effort cleared off the line at Middlesbrough on Tuesday.
Pleat added: "Stephen is one of the most dedicated and sincere boys that I've come across in football. He hardly ever misses a training session, plays with his heart and his head and has improved most definitely over the last two seasons."
Our director of football David Pleat has promised Spurs fans: "You've nothing to fear - we'll sort out a new deal for Stephen Carr as well."