The 35-year-old is in advanced talks with the Tractor Boys and a deal could be done by the weekend, the PA news agency is reporting.
McKenna was part of Ole Gunnar Solskjaer’s coaching team at Old Trafford and stayed on after the Norwegian was sacked in November.
Highly-rated United coach Martyn Pert is also expected to join McKenna at Portman Road as his assistant.
McKenna played for Tottenham’s academy before a hip injury ended his career early and he was part of Spurs’ youth coaching set-up before moving to Old Trafford, initially working with the Under-18s, and was promoted to the first team by Jose Mourinho in 2018.
They were dumped out of the FA Cup on Wednesday, losing 2-0 at Sky Bet League Two Barrow.
Former defender John McGreal was placed in interim charge and has drawn one and lost two of his three games.