The BBC is reporting that Terry is set to lose his captaincy after FA chairman David Bernstein on Thursday contacted all the other members of the 12-strong board to seek their views after the announcement that the defender's court case will not take place until July 9 - after Euro 2012.
Terry has been accused of racially abusing QPR's Anton Ferdinand, a charge which he denies.
More than one board member argued strongly that Terry should not be the England figurehead with such a serious charge hanging over him, and that the FA should act immediately rather than putting off a decision until the next board meeting on February 23.
The spectre of England being forced to make a complaint about racist abuse from the crowd when playing matches in Ukraine this summer has been raised - it would be difficult for the FA to take the moral high ground if England's captain is himself facing a criminal charge for racism.
Other board members believe the FA are in a no-win situation and that if they remove the England captaincy from Terry they will be accused of pre-judging the case and ignoring the principle of innocent until proven guilty. Terry's barrister on Wednesday entered a formal not guilty plea at Westminster Magistrates' Court.
England manager Fabio Capello is another factor and the Italian has previously insisted he should be the one making the decisions over the captain.
Some significant voices have been raised calling for Terry to stand aside. Damian Collins, a Tory MP who sits on the culture, media and sport committee and who has made a name for himself as a campaigner for FIFA reform, told Press Association Sport: "He is in a public position as England captain.
"Anyone else in a public position faced with such a criminal charge would stand aside from their position and then if cleared be able to return to that position. This has gone beyond being an allegation. He has been charged and has to appear in court and I don't think under those circumstances he can fulfil his duties. It is also what it means for communities across the country if people just close their eyes to the situation until after the court case."
Piara Powar, the executive director of European anti-discrimination body Football Against Racism in Europe (FARE), also believes the captaincy has to be removed, saying on Twitter: "Innocent until proven guilty. But should John Terry remain as England capt through the Euros? I can't see how he can."