A turbulent few weeks for the Blues was compounded on Thursday when news broke that Abramovich’s plans of putting the club on sale had to be put on hold.
Abramovich has been linked with Russia president Vladimir Putin, who is behind his country's unlawful invasion of Ukraine.
Among numerous repercussions for the sanctions, Chelsea will not be able to sign new players and contracts of existing players cannot be renewed, although the club have been granted a special license to continue operations.
Conte had a two-year spell in charge of Chelsea, winning the Premier League and FA Cup while Guardiola has had to battle with the Blues for top honours during his spell as Manchester City manager, and both have offered their sympathies.
"Honestly, I have just listened to this situation," Conte said ahead of Tottenham’s trip to Manchester United this weekend. "It's not easy. It's not easy.
"It's a pity also because I was coach in this club, in Chelsea. I enjoyed two seasons [there]. Also, I won two titles. It's a pity to listen to this situation.
"It's not simple for the players, it's not simple for [head coach] Thomas Tuchel, for the fans, for the whole environment.
"Honestly, I hope that in general that this situation between Russia and Ukraine is going to finish and to find peace, because it's much too important.
"Other situations that are coming from this conflict, I think that it's not right. I hope for the best, for this club, because I worked in this club, I enjoyed the two seasons.
"For sure, I love the team, the club that I worked in the past. Every team that I worked in the past, I hope for the best for them."
Guardiola added in his own press conference previewing Manchester City’s trip to Crystal Palace on Monday: "Of course with the position for the manager, for Thomas Tuchel and the players, it's uncomfortable, and I feel sorry for them because they're there to do their job as well as possible."
"For the rest, I don't know, I have to wait."
