Lampard guided Coventry to the Championship title on Tuesday with a 5-1 win over Portsmouth, securing promotion to the Premier League for the first time since 2000-01 and earning widespread recognition for one of the most impressive managerial turnarounds of the season.
Speaking to BBC CWR, King was careful not to dismiss the speculation but made clear he believes his manager is settled at the club. "He's done a fantastic job, it's been an incredible 18 months for us and for him. He's found a happy place at the moment."
"Everybody is going to get linked with everything, it's a merry-go-round. It's a bit disappointing clubs are appointing three or four managers a season. We don't want to be in those positions."
On the possibility of an approach: "I can't control it. I just think he's happy, I'm happy, everybody's happy, we've just got smiles on our faces and we don't worry about what may or may not happen for the head coach."
King also stressed that Coventry's approach to the Premier League would be measured rather than reckless. "People spend money very badly at times. A very expensive footballer might still be value — there are a lot of footballers who are very expensive but who are not value. Don't associate staying in the league and being very successful just with how much money you throw out of the door. I think that would be a mistake."
Lampard joined Coventry in November 2024, replacing the sacked Mark Robins with the club 17th in the Championship.