Packwood, 22, is a free agent after being released by Birmingham last month and joined the Red Bulls on trial earlier this week after failing to earn a contract with hometown club New England Revolution.
The American centre-back has impressed during his time training with the senior squad and Marsch has now revealed that he could be set for a long-term stay ahead of the MLS summer transfer window opening next month.
“We’re going to see what his availability is here moving forward, but we thought he did well and it was good having him here,” he said on Packwood. “We’ll see. There’s no decision yet. We’d like to continue to think about the possibility.”
Born in Concord, Massachusetts, to an English father and American mother, Packwood left the States in 2007 to join Birmingham as a trainee, before progressing though the club’s ranks to earn his professional debut in March 2012.
Labelled one of the Blues’ top prospects at the time, he looked set for a bright future at St Andrew’s but saw his progress hampered in 2013 after suffering a serious leg break during a third round FA Cup tie at Leeds United which kept him out for several months.
The club still handed him a contract extension during his spell on the sidelines but the New England-native would struggle to break back into the first-team upon his return to action and took in loan spells at Bristol Rovers, Colchester United and Cheltenham Town over the past two seasons before being let go.
Nevertheless, despite his recent struggles at the club level, Packwood remains a well-regarded talent within the USA setup and helped the Under-23s to a third place finish at the Toulon Tournament earlier this month.
The versatile centre-half, who can also operate at right-back or defensive midfielder, even earned a call-up to Jurgen Klinsmann’s senior squad in March 2014, when he was an unused substitute for a 2-0 defeat to Ukraine.
While he is still to receive a second call-up, a move to the Red Bulls, who have just freed up a roster spot after releasing fellow defender Andrew Jean-Baptiste, could well help get him back on the German’s radar moving forward.