The Chelsea legend has been out of work since his caretaker spell with the Blues - his second spell at the helm of his former club - ended in May 2023, and he could have his next team lined up.
According to Sky Sports News, "there has been no agreement reached yet" between Lampard and the Sky Blues, but discussions are said to be ongoing this week.
The retired footballer started his managerial career in 2018 with Derby County, before moving to Chelsea the following year until he was dismissed in 2021, and he then had a spell at Everton before returning to Chelsea for his caretaker stint.
Coventry are looking for a new manager following the sacking of Mark Robins on November 7 after over seven years in charge.
Since he left, Rhys Carr has taken over as interim boss, and secured a 2-2 draw against Sunderland in his first and only match thus far.
Last week, Coventry owner Doug King confirmed Lampard has applied for the role.
He told Sky Sports News: "We've received a huge amount of CVs from high-quality people, of which Frank is one.
"But the issue is we haven't done anything on that process, because we have been getting through this situation with the [fan] forum and focusing on making sure we were accessible and gave answers.
"However, clearly we are in the international break. We'll be assessing everything and then we'll work out who is going to make the shortlist, and then we'll interview."
King insisted he and his team wouldn't rush into an appointment, and Carr could be in charge for another "two or three" games if necessary.
He explained: "If we find the right person and we can all agree on what we want to agree then I think we can go pretty quickly.
"But if it isn't clear cut and we need to go deeper into certain things then it may take a bit longer."