Wigan boss Roberto Martinez has been charged by the FA this week for criticising referee Michael Oliver's performance during the Latics' defeat to Manchester United at Old Trafford.
And, despite admitting it is an "interesting" subject, the Portguese refused to be drawn on the Scot's relationship with officials.
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"It's an interesting question, but it's one that's impossible to respond to here," Villas-Boas told Sky Sports News.
"It would be brilliant to be able to answer it, but I paid a high fine last time and I don't want to again."The former Chelsea boss instead preferred to comment on in-form striker, Jermain Defoe, praising the 29-year-old's decisive contributions this season.
"He has been immense for the team," said the 34-year-old. "He's getting continuous opportunities that maybe he didn't have in the past so I think he is enjoying it a bit more. He is looking extremely happy.
"We have to be very grateful for what he has been doing for the team.
"For a striker goals are decisive and he has four in the Premier League. He's not far off being top scorer and he has been creating so much.
"I can't put anything of his in to question. He has desire, his motivation is there, and his movement is fantastic so we hope he will continue in this way."