Lady Catharine Popplewell, the wife of Mr Justice Popplewell, was on the board of the Independent Broadcasting Authority from 1987 to 1990. The two acquaintances, John Whitney and Lord Thomson, were, respectively, director-general and chairman.
They could be called to give evidence over Mr Aitken's involvement with TV-am. The former defence procurement minister and chief secretary to the Treasury has admitted during the hearing a "lack of candour" with the IBA over Saudi investment in the breakfast television company.
George Carman, QC, counsel for The Guardian and Granada Television, being sued by Mr Aitken over allegations that he was in the "pocket" of the Saudis, and pimped for them, told the judge that he did not foresee that Lady Popplewell would be called as a witness.
But he stressed that he could not give a "categorical undertaking" until all the documentation has been considered.
Mr Carman added: "You will accept that I am doing my best to try and obtain a concluding answer to that question as quickly as possible."
Mr Carman acknowledged that the judge had told counsel before the trial about his wife's membership of the IBA at the material time.
He added that if Lady Popplewell was called it would clearly have "unfortunate consequences" in terms of the trial for all parties.
Mr Carman continued: "I hasten to add, respectfully, this is through no fault of your Lordship. I want to make it abundantly plain to the court that speaking for myself and my clients one has total confidence in your lordship's integrity and impartiality.
"But equally I would be failing in my duty as a QC if I did not most respectfully say that I have some concerns which are shared by my clients of the public perception of the matter - that justice must not only be done but be seen to be done."
Mr Justice Popplewell said that if it had occurred to him that his wife was likely to be interviewed by any of the parties, he would not have refused Mr Carman's application on Thursday for a day's adjournment to consider what witnesses should be called following new evidence from the IBA.
The judge added: "I wouldn't have wanted to give any sort of appearance of seeking to prevent your client from taking a proof from my wife, or indeed in due course calling her, if she has anything material to say.
"If it transpires that my wife is to be called as a witness, we'll have to reconsider my position."
Mr Justice Popplewell added: "I might well be embarrassed if I had to decide whether Mr Whitney or Lord Thomson were telling the truth as opposed to Mr Aitken."
Mr Aitken had told the court how a television crew had chased him in his ministerial car, at one point necessitating a switch of cars.
However, Mr Carman Mr Carman produced television footage of the alleged incident which was shown in court, and he said the film did not show anyone chasing Mr Aitken.
Mr Justice Popplewell said: "What we see in the film did not constitute harassment."
The case continues.