The Crossmaglen ace - who starred for the club in their Ulster club SFC win over Kilcoo on Sunday - is being tipped to step into the breach left by Niall Carew, who took up the vacant Waterford manager's job last month.
In addition, Jason Ryan is expected to be added to the ticket as the team's trainer in McGeeney's new-look backroom team in what would be a considerable capture for Kildare.
The former Wexford boss ended his five-year association with the Model County after their Championship exit this year, initially intending to resume his club playing career in Waterford.
He was subsequently struck down with an anterior cruciate ligament injury and was linked with several of the then vacant managerial positions in Leinster.
Ryan insisted he wouldn't be involved with any team as manager, but hasn't ruled out coming on board somewhere in a more peripheral role and he is thought to be highly regarded by McGeeney.
He was reported to be on the cusp of agreeing to join the Lilywhites early last month but nothing official has emerged from Kildare.
John Rafferty - another Armagh man - spent a single season with McGeeney and has since departed while Carew, who initially agreed to stay on before reversing his decision, has taken up the top job in Waterford, leaving former Lily Damien Hendy as McGeeney's sole confirmed selector.
Part of Carew's role incorporated working with the Kildare forwards, a responsibility which would, in theory, be ideally suited to McConville, if the move transpires.
County chairman John McMahon told the Herald that the board expected to have a proposal for the finalised management team by the end of the week but was unwilling to comment on whether either McConville or Ryan would be part of the ticket.
In addition, McMahon insisted that Kildare were still determined to play all four of their scheduled home matches in next year's Allianz League Division 1 in St Conleth's Park, including a clash against Dublin on March 10.
The county grounds at Newbridge had its capacity previously reduced to approximately 6,200 because of health and safety requirements but they are actively looking to increase this figure, although the final decision rests with Croke Park.
"Our stance hasn't changed one bit," he stressed. "They're home games and they should be played at home."
The newly promoted Lilywhites are expecting to get word from the CCCC on the matter by the end of this week.