The Sky Blues sacked long-serving boss Mark Robins last week after a slow start to the season left the club 17th in the Championship.
talkSPORT understands Chelsea legend Lampard is the front runner to take the reins at the CBS Arena and will hold further talks this week.
Ruud van Nistelrooy, who has left Man United, has also applied for the job.
Coventry owner Doug King joined talkSPORT last week and didn't get into how good Lampard's chances of getting the job were but did admit that the former England, West Ham and Manchester City midfielder is a contender.
"We've received a huge amount of CVs from high-quality people of which Frank is one," King said.
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"We've done nothing on that process… but clearly we're in the international break, we'll be assessing everything.
"We'll work out who's going to make the shortlist and we'll go from there."
Lampard has been out of work since he finished his spell as interim Chelsea manager in 2023.
He had taken charge at Stamford Bridge for the second time after the sacking of Graham Potter.
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Lampard's last permanent role was with Everton.
He was sacked by the Toffees in January last year, leaving the club in 19th place in the Premier League at the time of his departure.
The former Chelsea star took charge of 44 games, and oversaw 24 defeats, 12 wins and eight draws.
His win percentage of 27.91 made him the second worst Everton manager of all time.
Lampard's permanent spell with Chelsea between July 2019 and January 2021 was more successful.
In his first season in charge, Chelsea scored 67 goals in 38 games, and were behind only Liverpool and Manchester City in the goalscoring charts.
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He led the team to a fourth-place finish in the Premier League and to the FA Cup final that season, with Chelsea losing to Arsenal at Wembley.
After 18 months in charge, he was sacked by the club he won the Premier League with as a player.
That was after the Blues suffered five defeats in their previous eight league games.
At the time, then-owner Roman Abramovich said Lampard's status as an 'important icon' of the club 'remained undiminished' despite his dismissal.
Lampard's first go at managing came at Derby in the 2018/19 season, with him taking charge of 57 matches, winning 24, drawing 17 and losing 16.
The Rams missed out on promotion to the Premier League via the Championship play-offs, but Lampard's managerial debut led to Chelsea snapping him up that summer.
He had been tipped to return to management with former club West Ham.
Now, he could be writing a new chapter with another second tier side, Coventry.
Frank Lampard is currently 2/7 favourite for the role with talkSPORT BET
The decision to sack Robins was criticised by a large number of Coventry fans, and even former EFL boss Neil Warnock labelled it as 'silly' and told the Sky Blues to be 'careful what they wished for'.
The Englishman was the third-longest serving manager in English football - after Manchester City's Pep Guardiola and Harrogate Town's Simon Weaver - following seven years and 244 days in charge of the Sky Blues.
Ironically, the final straw for the Coventry board came after a 2-1 loss at home to Lampard's former club, Derby.
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The Sky Blues have begun to turn their fortunes around after picking up a point on the road against league leaders Sunderland on Saturday.
Rhys Carr has been handed the interim head coach role until a permanent successor is confirmed.