Jennings, who has been in superb form for Tigers since joining the club in the summer of 2005, could win his first senior cap, while Cullen and Murphy will be looking to add to their respective tallies of 18 and 46 international appearances.
Jennings has been named alongside six other uncapped players in coach Eddie O'Sullivan's 30 man squad.
In the forwards, Jennings is joined by two other uncapped players in the shape of props Peter Bracken and Tony Buckley, while Cullen, Alan Quinlan and Stephen Ferris return to the Irish squad after missing out on the RBS 6 nations Championship.
Malcolm O'Kelly also returns to the squad having recovered from his knee injury that sidelined him for the entire championship. The twice capped Bernard Jackman is also named in the squad as one of three hookers on the touring party.
There are four uncapped players in the back division, with Tomas O'Leary and recent rugby league convert Brian Carney named in an Ireland squad for the first time.
"This tour was always about looking at options with the world cup in mind," said O'Sullivan. "It is an opportunity for players to put their cases forward for France.
"Argentina is always a tough place to tour and this will be no different. It gives us the chance to look at players in a pressurised Test match environment and as well as some experienced players, there are also some new prospects there who will benefit from the experience."
Ireland Squad
Forwards (17)
Neil Best (Belfast Harlequins/Ulster)
Simon Best (Belfast Harlequins/Ulster)
*Peter Bracken (Wasps)
*Tony Buckley (Shannon/Munster)
Leo Cullen (Leicester)
Stephen Ferris (Dungannon/Ulster)
Jerry Flannery (Shannon/Munster)
Keith Gleeson (St.Mary's College/Leinster)
Jamie Heaslip (Clontarf/Leinster)
Trevor Hogan (Shannon/Leinster)
Bernard Jackman (Clontarf/Leinster)
*Shane Jennings (Leicester)
Mick O'Driscoll (Cork Constitution/Munster)
Malcolm O'Kelly (St.Mary's College/Leinster)
Alan Quinlan (Shannon/Munster)
Frankie Sheahan (Cork Constitution/Munster)
Bryan Young (Ballymena/Ulster)
Backs (13)
Isaac Boss (Ballymena/Ulster)
Tommy Bowe (Belfast Harlequins/Munster)
*Brian Carney (Clonakilty/Munster)
Gavin Duffy (Galwegians/Connacht)
*Robert Kearney (UCD/Leinster)
Kieran Lewis (St.Mary's College/Leinster)
*Barry Murphy (U.L. Bohemians/Munster)
Geordan Murphy (Leicester)
*Tomas O'Leary (Dolphin/Munster)
Eoin Reddan (Wasps)
**Jeremy Staunton (Wasps)
Andrew Trimble (Ballymena/Ulster)
Paddy Wallace (Ballymena/Ulster)
N.B.
*indicates uncapped player
**subject to passing fitness test
