Ancelotti was sacked by Napoli on Tuesday just hours after leading his team to a 4-0 win to qualify for the Champions League knockout stages.
When quizzed on the reports at a press conference, Ljungberg responded: “I try just to concentrate on my job. Who the club decide to choose is totally up to them. I stay out of it.”
Ancelotti possesses a proven track record in England, having won the double with Arsenal’s London rivals Chelsea back in 2010.
Napoli released a statement announcing his sacking after the club’s win over Genk, adding: “The relationship of friendship, esteem and mutual respect between the club, its president Aurelio De Laurentiis and Carlo Ancelotti remain intact.”
Everton are also believed to be interested in hiring the Italian, as they seek a long-term replacement for Marco Silva.
Chelsea boss Frank Lampard gave his former boss Ancelotti a glowing recommendation when asked about the potential of him returning to England.
“I have huge respect for him, I am very sorry for him,” said Lampard.
“I know it was a tough job for him lately. I saw his interview before the game and I thought it was a very typically classy interview in what seemed a very tough time for him. He always handles himself brilliantly.
“I think he can work anywhere in the world at the top level, of course.”
Arsenal’s board are still undergoing an exhaustive process of finding a full-time manager, with ex-captains Patrick Vieira and Mikel Arteta, Bordeaux’s former Swansea boss Paulo Sousa, and Belgium boss Roberto Martinez all on a shortlist to be interviewed.
Ljungberg oversaw the Gunners’ win over West Ham on Monday, but his position is thought to only be temporary until the board can find the right candidate.
Following the interviews the four man panel tasked with finding the perfect recruit will then take their recommended candidate to Arsenal director Josh Kroenke, son of owner Stan and they will give it the green light.