Howarth and Stevenson have come through Clyde's youth system
Clyde youths Steven Howarth and Connor Stevenson are training with Rangers after impressing with the Second Division club's first-team.
And the Cumbernauld outfit do not rule out allowing striker Howarth and midfielder Stevenson, both 17, to move on should they impress.
However, they say that this would only be if it was in Clyde's interest.
Director of football Neil Watt also stressed that the pair would be "back with the squad for our next game".
Both players came through the Clyde youth system, with Stevenson, who signing a professional contract in February, becoming Clyde's youngest-ever player when he came on as a substitute against Queen of the South in April.
Howarth has been at Broadwood since under-12 level and has been a regular in the team's starting line-up this season.
Watt and manager John Brown agreed to allow the pair to train at Rangers' Murray Park training complex this week.
It is testament to Alan Upton and his coaches that SPL clubs are keeping regular tabs on what is going on at Clyde's youth academy
Clyde director of football Neil Watt
"Rangers FC recently contacted me to indicate that they would be interested in having a closer look, first hand," Watt told Clyde's website.
"Both players have recently made the step up from the club's youth academy to the first team and the club is keen to see them develop further, preferably with Clyde in the near future.
"We have been aware of Rangers interest for a while. But, when they formally made contact requesting permission to invite the boys to their training facility, John Brown and I discussed the matter at length.
"On one hand, we believe their development could best be served by continuing to be coached at Broadwood and push for regular first-team football.
"But we should not discount the opportunity for young players moving on if it serves them and Clyde FC best."
Howarth and Stevenson were given their chance when Clyde, who had been relegated from Division One, were forced to release their whole first-team squad to avoid going into administration.
Scottish champions Rangers are themselves deep in financial problems that prevented manager Walter Smith making any permanent additions to his squad during the summer.
"While SPL clubs are obviously set up to develop their own talent, they are nevertheless always on the lookout to supplement that," added Watt.
"It is testament to Alan Upton and his coaches that SPL clubs are keeping regular tabs on what is going on at Clyde's youth academy."
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