Arsenal are keen to remedy their awful run of form, which sees them just five points above the relegation zone.
The sacking of Unai Emery and instalment of Freddie Ljungberg as interim head coach has not had an immediate effect on results.
A draw away at Norwich and a home loss to Brighton have seen the Gunners slip further away from their goal of reaching the Champions League.
The North Londoners are reported to be pursuing a list of potential new head-coaches, including Leicester City's Brendan Rodgers.
Rodgers has guided Leicester to second in the Premier League table, in what has been the club's most successful season since the 2015/16 title run.
The Foxes win over Watford on Wednesday was their seventh on the trot and Jamie Vardy added to his league-best goalscoring tally.
But Arsenal have reportedly identified Rodgers as a top target to replace the departed Emery.
In a bid to close the door on the Gunners, Leicester are readying a new contract extension offer for Rodgers, according to The Telegraph.
The Northern Irishman only joined Leicester in February, signing from Celtic in a three-and-a-half-year deal worth £5m.
The deal was reported to have a £14m release clause inserted, which Arsenal would have to pay if they wanted to hire Rodgers.
Any new deal is understood to include a significant pay-rise and an increased buy-out clause to deter prospective employers.
When asked about the links to Arsenal, Rodgers was adamant he has everything he needs at Leicester.
"Why would I want to leave Leicester City at this moment in time? I’m working with a young group of players with so much potential, that want to improve and want to develop," he said.
"There’s a lot for us to grow and develop over these next few seasons. We’re moving to a new training facility.
"I respect there will always be this speculation around jobs, but I’m very happy here and have great relations with all the people, and I feel I want to continue with that."
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