The skipper, 28, missed the weekend win over Stoke after aggravating his back in the warm-up.
Terry is desperate to play in Saturday’s fourth round but may not train until tomorrow.
The Blues have crucial Premier League games with Middlesbrough and Liverpool next week so boss Phil Scolari may rest Terry against Ipswich.
Meanwhile, Spaniards Villarreal are preparing a £9million bid for Chelsea winger Florent Malouda, 28.
Malouda has flopped despite a promising start after he signed from Lyon for £13.5m in July 2007.