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.
A man stabbed to death at a London Underground station was a football fan on his way to a match, the BBC has been told.
The Arsenal supporter was killed in an “unprovoked attack” on the platform at Hillingdon station on Tuesday.
He had been on his way to the Emirates Stadium to see the Gunners face Nottingham Forest in the third round of the Carabao Cup, a source said.
It is the third murder investigation on the Tube network this year.
No arrests have been made over the attack, which Det Supt Gary Richardson described as “a shocking act of violence”.
He said the British Transport Police (BTP) investigation was in its “early stages”.
“We believe a group of young men were involved in an altercation on the platform before one of the men received a fatal stab wound,” he said.
Police were called to the station in west London shortly before 16:00 BST and the victim was pronounced dead at the scene.
Danielle Foster, who was driving past Hillingdon station at the time of the stabbing, said upon “hearing so many sirens, I knew something terrible had happened”.
“Lots of people were being turned away from the station as it had been closed,” she said, adding: “Then the police helicopter began circling the scene.”
Hillingdon station was closed by Transport for London (TfL) while police searched the area.
The station has since reopened.
So far in 2019 more than 110 murder investigations have been launched across London by the Metropolitan Police and BTP.