Lampard has been out of management since his short-term return to Stamford Bridge as caretaker manager ended after the conclusion of the 2022-23 season.
He has previous experience of the Championship having led Derby County to the play-off final in 2019 before going on to work at Chelsea and Everton in the Premier League.
Lampard is the current odds-on favourite with bookmakers, while former Sky Blues striker Robbie Keane has also been listed as a potential contender, following his time in the Indian Super League and with Maccabi Tel Aviv, which ended in June.
Ex-Coventry midfielder Lee Carsley, the current England Under-21 coach, whose role as interim boss of the full England men’s team is scheduled to come to an end next week, has been linked, along with Matt Bloomfield, boss of League One leaders Wycombe Wanderers.
Bloomfield told BBC Three Counties Radio on Saturday: “I’ve not heard anything from my club. It’s just speculation as far as I’m concerned. But it’s lovely to be linked with jobs higher up the food chain because it shows that the job you’re doing is the right one.”
When advertising the vacancy, following the decision to part company with Robins last Thursday morning, the club said that it would, “take its time to appoint a successor to Mark, although the position will be that of head coach working within the new structure set up by the club over the last two years.”
King made joint first-team coach Rhys Carr caretaker boss for Saturday’s trip to Sunderland.
After coming back from 2-0 down to draw with the league leaders, King confirmed on Monday night that former Wolves development coach Carr will remain in the post until a permanent successor has been found.
City’s next game is the lunchtime home date with second-placed Sheffield United on Saturday 23 November.