Mr Barrow, 62, stepped down in a surprise move on Friday, just weeks after he was found to have breached the council's code of conduct over the declaration of a business interest.
In a further development, West Mercia Police confirmed over the weekend it had received a complaint against a Shropshire man over alleged "misconduct in a public office", which is believed to relate to Mr Barrow, who lives in Trefonen, near Oswestry.
A statement said: "West Mercia Police can confirm we have received a complaint regarding misconduct in a public office involving a man from Shropshire."
Mr Barrow's former Conservative Party colleagues were meeting today to nominate their new leader, with interim leader Councillor Steve Charmley the favourite to take the role. If Mr Charmley secures the nomination he would then require formal election as leader of the council at its full meeting on December 17.
Speaking to the Shropshire Star ahead of the meeting Councillor Charmley paid tribute to the former leader but said he understood his decision to resign.
He said: "He did a fantastic job for the county but it is a long time to be in the job – six-and-a-half, seven years, and it does wear you down.
"Keith's legacy is that he led this council through the difficult years and Shrewsbury University will stand as a long-lasting tribute to his leadership."
Councillor Lee Chapman, the authority's cabinet member for adult social care, said he too could understand Mr Barrow's decision.
He said: "I think after the standards board report there was always the possibility that Keith would decide that he no longer wanted to remain as leader so while I would not have put money on him resigning, I can understand him him taking the decision he did in light of what has happened."
Councillor Chapman would not be drawn on who he would be supporting for the leadership nomination, although he said whoever was chosen would face significant challenges in light of the council's financial position.
He said: "Clearly the group needs to agree how best we go forward and we do that in a democratic way. We will discuss it between ourselves and decide what is best for Shropshire Council going forward.
"The responsibility is a big one. We continue to have significant challenges and issues around the budget and we need to make sure that we are led strongly and that we go forward from here."
Liberal Democrat Councillor Andy Boddington, who represents Ludlow North, called for a "new broom" at the council following Mr Barrow's resignation.
He said: "I would say it is time for a complete change. We need a leader who will create consensus in the council and across the county. We need a completely new broom."
Mr Barrow was not available for comment.