The evidence surfaces in a memo in declassified files from that year that have just been released in Belfast.
In a minute to officials dated 15 January 1988, Rosalind Earnshaw, private secretary to Brian Mawhinney, the Northern Ireland junior minister, reported on a conversation.
It was between Dr Mawhinney and SDLP MPs Seamus Mallon and Eddie McGrady.
"While the MPs used their leader's argument in defending the meeting, the minister was impressed with the lack of enthusiasm by which they put forward the argument and what appeared to him to be their embarrassment/discomforture."
Ms Earnshaw wrote: "In response to Dr Mawhinney saying to Mr McGrady that he found it difficult to reconcile his recent statement regarding the relationship of the SDLP and Sinn Féin with John Hume's meeting, Mr McGrady looked down at the table, said the two were not irreconcilable, but made no attempt to reconcile them."
SDLP deputy leader Mr Mallon said that "whatever else was the outcome of the Hume-Adams meeting", Mr Hume would "not allow himself to be wrong-footed".
The first meeting between SDLP leader John Hume and Sinn Féin leader Gerry Adams on 11 January 1988 did not find favour with Mr Hume's senior colleagues in his party.