The double-header will start with the visit of Serbia to Croke Park in Dublin on May 24, with the clash with Colombia being held at Craven Cottage in London on May 29.
Murphy has only one international cap to his name, but Trapattoni has promised his entire squad they will get the chance to impress him on the pitch.
"We will have two training games in Portugal and the games against Serbia and Colombia so I will get to see all the players playing," he said.
"The next two weeks are important. It is my first opportunity to work with the players and I am looking forward to it.
"Our squad has a lot of young players and, from my experience, they are hungry to learn."
West Brom's Dean Kiely and Birmingham's Colin Doyle are the other two keepers in the squad, with the first-choice stopper Shay Given ruled out through injury.
The former Iron forward Andy Keogh, now at Wolves, is also in the squad.
Squad in full: Colin Doyle, Dean Kiely, Joe Murphy, Alex Bruce, Damien Delaney, Richard Dunne, Kevin Foley, Stephen Kelly, Paul McShane, Darren O Dea, John O Shea, Damien Duff, Owen Garvan, Darron Gibson, Wes Hoolahan, Stephen Hunt, Aiden McGeady, Stephen McPhail, Liam Miller, Darren Potter, Andy Reid, Martin Rowlands, Sean Scannell, Glen Whelan, Kevin Doyle, Robbie Keane, Andy Keogh, Shane Long, Daryl Murphy.