The young Magpies will discover their opponents on Wednesday, when the two sides meet at Fratton Park.
Pompey breezed past local rivals Eastleigh to book their place in the Second Round, while the Met have already had to see off four different sides to reach the same stage, having entered in the competition's Preliminary Round.
Dave Watson's charges will be looking to improve on their showing in last season's Youth Cup, when they were eliminated by AFC Wimbledon in the last 32.
This time out, the Magpies' Third Round tie will be played before Saturday 7th January.