LeMond, 52, is the only American winner of the Tour after Armstrong was stripped of his seven titles in 2012 for systematic doping.
"If he was clean and everybody else was clean, he's a top-30 [Tour finisher] at best," LeMond told CNN.
"He's not capable of winning the Tour, he's not capable of the top five."
Armstrong, 42, was also banned for life following a United States Anti-Doping Agency investigation into the doping practices of the United States Postal Service team, a punishment LeMond feels is fair.
"There are people who are criminals who just shouldn't be able to participate again in anything," he said.
"It's like [jailed financier] Bernie Madoff - should he be allowed to come in and be a part of Wall Street managing money? No, he shouldn't.
"And that's [the case] with Armstrong. He shouldn't be allowed to be back in sport."

The caves have been digitally reproduced as part of the city's first Festival of Caves.
The tour will take in Mortimer's Hole under Nottingham Castle and King David's Dungeon - caves some people would not be able to access.
The city has more than 500 man-made sandstone caves which have been used for dwellings and jail cells.
Nottingham City councillor, Dave Trimble, said: "There are plenty of local people who don't know about the hidden world beneath their feet."
He said the new virtual reality tour would allow visitors who were unable to descend the steep steps into the caves to experience them.
Andrew Whitney of Hot Knife Digital Media, which developed the tour, said: "We've taken very accurate data to digitally reproduce the caves in a gaming environment.
"We're excited to bring the caves into the 21st Century using the latest gaming and virtual reality technology, increasing the accessibility of these sites to everyone."
A series of caves has been found in the past six years due to funded projects such the Nottingham Caves Survey, which mapped and laser-scanned many of them.
The festival runs until 23 October.

All 57 seats were contested, of which the Tories took 43, compared to the 36 they won in 2013.
Labour gained a councillor, taking their tally to 12, while the Liberal Democrats saw their number of seats fall from six to two.
There will be no UKIP representatives on the council - all three of their seats were Tory gains.
Turnout was up on 2013, at 33.7%.
Heather Smith, Conservative leader on the council, said: "I'm very pleased. We've exceeded our number from four years ago and our target of 40 seats.
"We expected turnout to be low because of the general election.
"I can't foresee a bigger majority will make a difference [to how we govern]. We have to work within a certain budget."
In Northamptonshire, the Conservative party gained 8,832 votes in the local election - 45.54% of the vote.
It is higher than the national projected vote share for the Tories, which stands at 38%.
The Liberal Democrats suffered a major blow when their local leader, Brendan Glynane, lost his Delapre and Rushmere seat to Labour.
Asked about the increased Conservative majority, Mr Glynane said: "I think they will be emboldened by this.
"The finances are not sorted, there is nothing left in the bank and I think you will see some severe cuts."
As the declaration of results drew to a close, John McGhee announced he was to stand down as Labour group leader on the council.
Mr McGhee won his Kingswood ward, but said: "It's been extremely difficult watching the destruction of public services in Northamptonshire.
"I decided [to stand down] well before this election. I've been doing it so long. It has nothing to do with today's results."
Three-time winner Greg LeMond believes Lance Armstrong was only capable of a top-30 Tour de France finish "at best" without performance-enhancing drugs.
[NEXT_CONCEPT]
Nottingham's network of caves has been turned into a virtual reality tour, to open them up to a wider audience.
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The Conservatives have increased their control of Northamptonshire County Council.