Arsenal have identified Wolves boss Nuno Espirito Santo as a potential replacement for Unai Emery if the Gunners decide to sack the Spaniard.
Head coach Emery is under pressure after a winless run of six matches across all competitions.
Arsenal have only won four of 13 Premier League games this season.
BBC Sport understands that if Emery is sacked and Nuno is allowed to speak to Arsenal, then the Portuguese would be a strong contender to take over.
Nuno said it would be “disrespectful” to talk about being linked with Arsenal when asked in a news conference before his side’s Europa League tie against Braga on Thursday.
“I wouldn’t ever mention an issue which is not a reality,” he said. “Speaking about a job which has a manager would be disrespectful and I will not do so.”
Emery said he still has the full support of the club, having been warned results must improve while being offered public backing by the Arsenal hierarchy earlier this month.
“Really the club is supporting me,” he said. “I feel the club, everyone responsible in that area, is backing me. Really I appreciate it a lot.
“I feel strong with that support and know my responsibility to come back and change that situation.”
The former Sevilla and Paris St-Germain boss added he is only focused on “today and tomorrow” as he prepares for his side’s Europa League match at home to Eintracht Frankfurt on Thursday.
“My job is to prepare for the match, to show the best performance in front of our supporters,” he said.
Arsenal go into Thursday’s game top of Group F, four points clear of both their German opponents and Standard Liege.
On Sunday, a number of Arsenal fan groups called for “urgent action” over the “state of things” at the club.
“My focus is only today and tomorrow, to do all the things that we have worked on here at the training ground,” Emery added.
“We know our supporters were disappointed by the draw against Southampton, but we have the perfect chance to reconnect with our supporters.
“Our wish is that every supporter tomorrow helps the team, we need them.”
Arsenal are also eight points adrift of the top four and 19 points behind Premier League leaders Liverpool.