The England and Wales Cricket Board are keen to remain tight-lipped about their planned discussions with Pietersen, who was dropped from the Test squad earlier this month due to what team director Andy Flower described as issues of "trust and mutual respect". Morgan is one of a handful of one-day specialists drafted in for the NatWest Series against South Africa.
Speaking ahead of the second ODI at the Ageas Bowl on Tuesday, the Dubliner said: "I think Kevin is a world-class cricketer and any team around the world would want him in their side, but there are issues surrounding him at the moment and it will take time to resolve them. Obviously the quicker that happens the better."
He added: "Personally I didn't find him difficult but I've not been around the Test team a lot.
"I think that it is hugely important because the amount of time we spend together is huge. We spend more time together than with our families, particularly on tour. It is a huge factor and it has been for the last number of years - successful years we've had as the England cricket team."
England's one-day side have already had experience of coping without Pietersen's undoubted skills, winning all six completed matches since his surprise retirement from limited-overs cricket.
That was later reversed - albeit via an ill-conceived YouTube clip - but a 2-0 series win over West Indies and a highly-impressive 4-0 defeat of Australia suggest a recall is not a necessity.
And Morgan, a senior figure in the white-ball side despite his current absence from the Test reckoning, has been impressed by the strength in depth highlighted by Pietersen's exit.
"I think we've played fantastic cricket," he said. "The guys who have come in and replaced him have done particularly well. Whoever has stepped up has done really, really well.
"That's been important to the winning run we've had, particularly against a top side like Australia. We've built some great blocks towards where we want to be in our progress as a one-day side. I think we have a lot of match-winners."