Many names have been linked with the Roma hotseat next season and Andreazzoli's own future has been cast in doubt, but he knows he can have little influence on the rumours.
"All coaches are judged by results, sometimes a bit too much, but all I can repeat is that it is not something which worries me," he said.
"All I am thinking about is improving the results.
"We have made some extreme improvements in many aspects, we just need to be a bit more consistent."
Roma are currently fifth in the table and on course for a place in the Europa League, which would boost Andreazzoli's chances of remaining in charge next season, even if a lot can still change in the final three matches of the campaign.
"I only look at the final standings, not intermediary ones," he said.
"I think we would deserve a few points more than what we have, but we are happy and we want to improve our position tomorrow [Tuesday]."
That is not going to be as easy as the league table may suggest, though, with the 18-point advantage over opponents Chievo giving little indication as to how hard the Flying Donkeys are to break down.
"Chievo are a side to respect," he said. "All our opponents must be feared and respected, no matter what the league table says.
"But given the impressions I have gained from training, I am encouraged by what I have seen."
Chievo coach Eugenio Corini is encouraged by his side reaching 40 points at the weekend, but is not convinced that will be enough to guarantee them safety.
"Arithmetically, we still need two more points," he said. "If Palermo were to win their remaining games, they would reach 41 points, and we are behind them on our head-to-head record so we still need to get more points.
"We're going to try to get them at the Stadio Olimpico tomorrow night [Tuesday]."