Having withdrawn his application to renew his UK visa, Abramovich has since made his home in Israel after being granted citizenship there. The 52-year-old has previously invested in Israel and it was reported last year that he would be exempt from paying tax for the first 10 years.
"Everything he's doing reaffirms his commitment to Chelsea," the chairman told Sky Sports.
"We hear from him several times a day and he's talking to us about players, commercial activities and our good causes. So I would say he's committed to Chelsea."
Abramovich, who is Jewish and has donated to the Holocaust Galleries exhibition set to open at the Imperial War Museum in 2021, is also keen for Chelsea to tackle anti-Semitism after a couple of recent incidents have been highlighted.
"It was his idea and he's checking in with us regularly as to how it's going and what we're doing and what effect we're having, so yes it's very important to him," Buck explained.
"We had a couple of incidents and we were very unhappy with it, particularly since the club now is very focused on a project thanks to the impetus from Roman Abramovich of tackling anti-Semitism."
On the pitch, Chelsea have been struggling by their own high standards. The appointment of new manager Maurizio Sarri hasn't been the success officials and fans hoped it would be and the club is in danger of missing out on the Champions League for the third time in four years.
Chelsea are also subject to a FIFA-imposed transfer ban that is set to prevent them from being able to register new players this summer or next January, potentially having a hugely detrimental impact at a crucial time when squad rebuilding is badly needed.