The Financial Services Authority demanded more "openness" from Bob Diamond when it approved his appointment as chief executive of Barclays in September 2010.

Memos and correspondence published by the Treasury select committee on Wednesday in the wake of Diamond's resignation over the Libor scandal also reveal that the FSA was aware of an investigation into the rigging of the key interest rate when it authorised his promotion.

When the £290m fine for Libor-fixing was announced in June this year, Diamond was not found to be involved. But he left five days later, after Bank of England governor Sir Mervyn King intervened to say that regulators had lost confidence in the Barclays boss.

One memo released on Wednesday shows that the then-head of the FSA, Hector Sants, told Marcus Agius, who will step down as Barclays chairman next month, that the regulator's attitude towards Diamond could harden once the Libor investigation was completed.

The memo was released after Sants wrote to the committee to take issue with Agius's assertion that the Libor affair had not been discussed at the time of Diamond's promotion. "I specifically made clear that we reserved the right to reassess [Diamond's] suitability in the light of the conclusions reached by this investigation and requested he made this clear to Mr Diamond," said Sants in a letter to the committee chairman, Andrew Tyrie.

"I made clear that our concerns about Barclays culture were not some generic observation but specific to Barclays and asked that these concerns be communicated by Mr Agius to Mr Diamond," Sants wrote.

The FSA's record of Sants's meeting with Agius in September 2010 reveals the Barclays chairman acknowledging that Diamond had lost out on the chief executive role six years earlier, when John Varley won the top job, and that Varley had agreed to be a mentor to his successor before quitting at the end of December 2010.

Identifying the executives involved by their initials, the FSA's record of the meeting says: "JV will … coach BD in his remaining six months. MA added that whilst BD is very competitive and lost out in the previous CEO selection to JV he suspects we will now see him mature and relaxed given he has now achieved his goal.

"HS explained that the relationship with BD had not reached the level of openness, transparency and willingness to air issues with the FSA [as] has been the case with John Varley. BD therefore needs further development in this area as he steps up to CEO. BD did not disagree with this point in the interview process and undertook to address," the memo said.

It also shows Sants told Agius of the FSA's concerns about succession planning in Barclays Capital, the investment banking business that Diamond was then running, following Diamond's promotion to the top job.

Sants also indicated the regulator was concerned that the division that had raised most alarm bells about risk at Barclays – the investment bank – was the one being run by Diamond at the time.

"HS explained the FSA's historical concerns regarding Barclays risk appetite and control framework. He acknowledged the progress made by JV and the work underway addressing the FSA concerns. However at the time of the FSA concerns BD was managing the area within the group where the concerns were foremost therefore it is important that in his new role as CEO he ensure the continued progress of initiatives the group has commenced," the memo said.

Agius told Sants that Diamond was "on board" and that it was the "collective judgement of the board that BD will rise to these challenges and succeed".