In correspondence seen by The TES, sources from the lecturers' union Natfhe have expressed concern that a recruitment campaign was taking place at Warrington collegiate institute.
The active attempt to recruit members from other unions would contravene the anti-poaching Bridlington agreement, in place between TUC-affiliated unions since 1939.
There have been reports by Natfhe members that a representative of another trade union has approached them, suggesting they transfer their affiliation and allegiance to them.
Suspicions grew after five of their members at Warrington collegiate left Natfhe to join the GMB.
Members of Natfhe were also informed during a meeting with the college principal that informal conversations had taken place about the GMB seeking a local recognition agreement.
College principal Paul Hafren acknowledges that informal discussions have taken place with a member of GMB, which would allow it to officially represent teaching staff at the college. Mr Hafren claims, however, that this individual has no representative rights within the organisation.
He says a local recognition agreement would not be considered unless the union represented more than 50 members of the teaching staff at the college. But he does not anticipate that this will happen.
"Natfhe has a strong tradition of representation at Warrington which works well here and throughout the country," he said.
Mr Hafren said that he had not had a formal application from GMB and believed that the source of the dispute was likely to come from the actions of a former Natfhe member who joined GMB after disagreements with local members of the union.
Duncan Edwards, a spokesperson for the GMB in Lancaster, has denied any knowledge of such activities.
He said: "The GMB has not made any campaign to recruit lecturers. If people want to join us because they agree with our principles, then they can. We have very good relationships between the institute and Natfhe and we wish to maintain those."
Colin Gledhill, regional officer for Natfhe, says general secretary Kevin Curran has reassured him that the GMB has no ambitions to recruit professional educators. But he said: "We are still concerned that one local activist appears unwilling to accept this and we are not satisfied that he has stopped."