Villas-Boas has given the green light for Zhirkov to leave as he starts to restructure the Premier League club's squad and he believes the transfer is almost completed.
"Yury is in between reaching a full agreement, between club and player, with Anzhi and in the end it was mostly his decision," Villas-Boas said after Saturday's 3-1 friendly win at Rangers.
"It is a great financial offer for him, it is a return home and I think he has decided to part company."
Zhirkov's departure could be the prelude to a busy few weeks in the transfer market for Villas-Boas, but he refused to be drawn on reports that Chelsea will make a third improved offer for Tottenham's Croatian midfielder Luka Modric.
"I have been answering a lot about it and I won't make any further comment," he said.
Villas-Boas gave a more revealing answer when asked about his interest in Anderlecht striker Romelu Lukaku.
Chelsea have been monitoring Lukaku for some time and the Blues reportedly had an ?£18 million offer turned down for the player last month.
"He is a very interesting young prospect and the situation is now that we have to position ourselves to maybe get this kind of talent. So I would say that anything can happen," Villas-Boas said.
The Portguese coach also praised England Under-21 striker Daniel Sturridge, who was on loan to Bolton in the second half of last season but looks set to feature in Chelsea's plans this year.
"He has been sparking in this pre-season. It is nothing new, it is what he was doing in Bolton and he deserves his chance," Villas-Boas said after seeing Sturridge score twice on Saturday.
"He has been showing his qualities and we will count on him this season with a different perspective."
However, Villas-Boas could be without John Obi Mikel for the opening game of the Premier League season at Stoke next Sunday after the Nigeria midfielder aggravated an injury against Rangers.
"He had a knock which he suffered a few days ago in training," Villas-Boas said. "He had an injection before the game to avoid pain but it was getting pretty nasty for him and we decided to take him out of the game.
"We will evaluate the situation and make a decision because he is one of our players involved in the international break."
Source: AFP
Source: AFP