Coventry, who has some links with the South, having studied at the University of Otago in the 1980s, playing one game for Otago in 1987, has just finished his first season as head coach with London Irish in the English Premiership.
It was not a season to remember for Coventry with London Irish relegated from the Premiership, having won just four out of 22 games.
Despite the forgettable season, Coventry has been given full backing by his bosses as the team heads down to play in the second-tier Championship section.
But with the expected loss of income and exodus of players, Coventry may decide to seek new pastures.
The Highlanders job would appeal and his nous with forward play would be a good fit to replace head coach Jamie Joseph, who also coaches the forwards.
Tony Brown has signed a contract to continues as assistant coach next year while assistant coach Scott McLeod - who looks after defence - has yet to sign a contract for next season.
Coventry was highly regarded in New Zealand rugby circles before he left for England.
He was the forwards coach for the Hawkes Bay side before moving to the Chiefs, when Dave Rennie arrived in 2012.
The team had instant success, winning the Super rugby title in 2012 and 2013.
Coventry left to coach London Irish after the 2015 season.
London Irish had a sprinkerling of New Zealanders including former All Black prop Ben Franks and former Highlanders Chris Noakes and Halani Aulika.
Highlanders chief executive Roger Clark said he would not be commenting on the coaching position.
Meanwhile, the Highlanders have sold 11,000 tickets for the game against the Chiefs on July 16.
Clark said ticket sales were brisk and a big crowd was expected.
The game against the Crusaders last week had sold out and Clark said he hoped to get another good crowd for the game, the final scheduled home match of the season.
The Highlanders will not be opening the Otago Daily Times end of the stadium for temporary seating. Clark said the cost to put up the seats was high and it was doubtful the crowd would be big enough to cover the costs.
