Edinburgh moved up to eighth spot at the weekend, beating Newport Gwent Dragons 24-10, but the win came at a cost.
Cornell Du Preez is set for a lengthy spell on the sidelines after a bad leg injury, while David Denton and Fraser McKenzie are also still out.
The strain on Edinburgh's back row means head coach Alan Solomons only has Mike Coman, Hamish Watson and Roddy Grantavailable to challenge Leonardi for a starting spot.
But the 27-year-old is thrilled he is getting the chance to make an impact on the pitch, and hopes getting game-time at BT Murrayfield will help him muscle his way into Daniel Hourcade's plans for the Pumas autumn international there on November 8.
"I am not feeling the pressure, I am just enjoying getting opportunities to play," he told the Edinburgh Evening News.
"For me it is really nice to be involved in a run of matches and I just have to keep doing my best for the team.
"All rugby players train all week to play a match at the end of it and I always want to be involved in the squad when I can be.
"I have played mainly flanker here, but I have also played No.8 a lot back in my own country and for Argentina and I am happy to play in any of the three positions.
"I am always in touch with the head coach and his staff from Argentina. I was not involved in the Rugby Championship as the coach wanted to try out some new guys to improve the base of Argentinian rugby. I understood that.
"I am always working hard and trying to do my best and hopefully I may get another opportunity to play for my country again next month.
"On my first tour with Argentina back in 2009 I was playing against Scotland at Murrayfield when we won 9-6 and that was a good experience, so maybe soon I will get the chance to do the same again."
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