The Championship club has been without a manager since McCarthy abruptly left four games before the end of the season and have since received 100 applications for the role.
However, it seems Lampard could be a credible candidate after allegedly already being interviewed twice by owner Marcus Evans.
St. Mirren's Jack Ross and Shrewsbury Town's Paul Hurst are also on Ipswich's shortlist with talks already taking place.
If Lampard was to get the job, it would be his first stab at management after nothing materialised to links with the Oxford City job earlier in the year.