The 31-year-old, who departed Portman Road for Newcastle United 11 years ago, is available on a free transfer after leaving Sunderland at the end of last season.
Bramble turned out for Ipswich in a pre-season friendly against Gillingham on Tuesday, with McCarthy admitting that he is interested in acquiring the defender's signature.
"Titus did what Titus had to do. I only met up with Titus for the first time at our pre-match meal. He asked if he could come in for training and wanted to play," McCarthy told the club's official website.
"He's obviously interested in coming here and we are interested in him otherwise he wouldn't be playing for us. He showed a good commitment to come and play but it's early days yet. No more than that."
Bramble had previously trained with West Ham United earlier in the summer.