The Scottish Premiership club parted company with Mark Warburton on Friday.
McLeish, who was manager for five years until 2006, insisted there has been no contact with his former club.
But the 58-year-old told Sky Sports: "When you get asked to come to a club like Rangers then its for sure a decision to turn that down."
McLeish, who was sacked by Egyptian Premier League club Zamalek in May, has emerged as the bookmakers' favourite.
And he was a television guest as Rangers, with caretaker Graeme Murty in charge, defeated Greenock Morton 2-1 to reach the Scottish Cup quarter-finals.
Asked if he was likely to be the new manager, McLeish replied: "You never know. It is purely coincidence that I'm here today.
"You called me a couple of weeks ago to come and do this game and I then find there's been some events happening at Ibrox the last couple of days."
McLeish was also asked if Rangers had been in touch since Warburton departed on Friday.
"No," he said. "Obviously there's a lot of speculation, but at the moment there's nothing I can update you on apart form the fact that I'm here and it looks more than a coincidence, but it is a coincidence."
McLeish won two Scottish titles as Rangers manager and the Glasgow club also won five knock-out trophies during his tenure - the Scottish Cup twice and League Cup three times.
The man who has also managed Motherwell, Hibernian, Scotland, Birmingham City, Aston Villa, Nottingham Forest and Genk hinted that a return to Ibrox would be an attractive prospect.
"I am a Rangers man, so you obviously have to keep that in consideration," he added.
Rangers chairman Dave King has claimed that the club accepted Warburton's resignation after the manager's representative had talks with Nottingham Forest, while the Englishman denies he resigned.
The Glasgow side lie third in the Scottish Premiership, 27 points adrift of city rivals and holders Celtic, and King said Warburton's team had not reached the targets expected of them.
Former Rangers players Gordon Smith and Barry and Derek Ferguson have described McLeish as the ideal candidate to take over.

The dig at Auckland Castle's walled garden revealed a pioneering pinery-vinery, created by Bishop Richard Trevor in the 1750s.
This utilised furnaces and flues to allow the cultivation of exotic fruits, particularly much coveted pineapples.
It is believed to be one of the first of its kind in the North East and set the standard for following ones.
The dig, by archaeologists from Durham University and volunteers from the Auckland Castle Trust, was in advance of a Â£10m scheme to grow fruit and vegetables under glass domes in the walled garden to supply a new on-site restaurant.

Cardiff council has issued travel advice to drivers, with roads shutting from 06:30 BST and reopening at about 12:30.
East Tyndall Street, Lloyd George Avenue and Bute Place are among those being closed for the triathlon.
Drivers heading to the Extreme Sailing event before midday have been advised to follow signposted routes to the bay.
The council said the best route to get to the sailing would be the A4232, exiting at the junction for Mermaid Quay and the central link road.
A cycle diversion is also in place around Britannia Park, between Cardiff Bay and the barrage.
Roads closed during the triathlon:

David Miller, 56, died at his house on Patterdale Walk, Northampton, in the early hours of Tuesday.
Northamptonshire Police said the woman was 39 and of no fixed address.
Four others have been charged with murder: Zena Kane, 35; Ian Cuthbertson, 49; Michael Hallett, 37 and Joseph Catlin, 30, who were remanded in custody at Northampton Crown Court.
Alex McLeish admits he would find it difficult to turn down Rangers should he be asked to become manager at Ibrox for a second time.
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Heating systems to grow fruit have been uncovered at the former private palace of the Prince Bishops of Durham.
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Road closures have been announced ahead of Cardiff Bay's triathlon and sailing events on Sunday.
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A woman has been arrested on suspicion of the murder of a man who was stabbed to death at his home.