The Dons say the forward will spend a couple of days with the club and is "just one of a number of players the manager will assess in the weeks before the season comes to a close".
Murphy began his career with Arsenal but did not make the breakthrough, although he gained first-team experience on loan with Preston and Brentford.
The 22-year-old represented his native England at several age levels before switching allegiance to the Republic of Ireland and has spent this season playing for Telstar in the Dutch second tier.
Despite the trial move, assistant manager Tony Docherty has told all the current Aberdeen players they still have the chance to ensure they remain at Pittodrie next season.
McInnes and Docherty take charge of their third game when Aberdeen play Dundee at Dens Park tomorrow and are looking to build on two clean sheets.
Docherty told RedTV: "Of course, we have identified players. Recruitment is important for the club so we wouldn't be doing our job if we've not done that. But recruitment starts from within, so the players that are here at the moment we're getting to see them on a daily basis which is great, and watch this space."
Docherty also gave further encouragement to the young players at Pittodrie after 17-year-old midfielder Craig Storie made his debut in last weekend's 1-0 victory over Kilmarnock.
Docherty added: "I've got to say there's many things we've been impressed with at the club since arriving but certainly the under-20s, having just cemented second place in the league, and every game we've been at we come away feeling enthused and excited by these young players in terms of the future for Aberdeen.
"There is real quality in the under-20s and it bodes well for Aberdeen Football Club."