French-born inquiry counsel Carine Patry Hoskins, who was raised and educated in Glasgow, and Hugh Grant's representative David Sherborne allegedly had a relationship and holidayed in Greece.
It reportedly came days after the public hearings concluded and months before the inquiry ended.
The Bar Standards Board said complaints about the pair had been investigated, but its Professional Conduct Committee decided there was no "realistic prospect" that a disciplinary tribunal would make a finding of professional misconduct.
Sir Brian Leveson has already rejected suggestions that his report into press standards may have been tainted by the alleged relationship between the two barristers.
Mr Sherborne, who also represented other alleged phone hacking victims, and Ms Patry Hoskins, maintain that their relationship did not begin until after the judge's report was published in November 2012.
MP Rob Wilson wrote to the Bar Standards Board asking them to consider whether there may have been a breach of its code of conduct as a result of personal relations between Ms Patry Hoskins and Mr Sherborne.
A board spokesman said: "The complaints about Mr David Sherborne and Ms Carine Patry were considered by the Bar Standards Board's Professional Conduct Committee following an investigation.
"The committee concluded that there was no realistic prospect that a Disciplinary Tribunal would make a finding of professional misconduct in relation to any of the aspects of complaint and the complaints were dismissed.
"We do not normally comment on individual cases unless a Disciplinary Tribunal has been scheduled. However, on this occasion, as so much information is already in the public domain it is clearly in the public interest to make this statement."
Earlier this year Sir Brian insisted that "every finding of fact, every conclusion and every recommendation" in last year's report was his alone and that Ms Patry Hoskins had no influence over them.
Writing to Mr Wilson earlier this year, he said: "Ms Patry Hoskins was second junior counsel to my inquiry and, throughout the process, undertook all of her work at the request and under the direction of either myself or Robert Jay QC.
"You ask whether it is possible that she may have had an input into the inquiry's conclusions prior to August 3 2012: the answer is 'no'."