Parrish has been sidelined in recent weeks with a thigh problem and will be assessed ahead of the trip to Underhill.
The Shrimps are enjoying a rich vein of form, winning five of their past eight matches, but goalkeeper Barry Roche believes the struggling Bees will provide them with a stern test.
He told Press Association Sport: "It's always tough when you go to Barnet, no matter what position they are in the league, it's always a tough place to go.
"We've seen that over recent years where we've had a couple of really good battles with them.
"They're in desperate need of the points so it's a good game and a game we're all looking forward to."
Forward Jordan Burrow is pushing for inclusion after bagging a brace during Morecambe's 2-0 reserve win over Tranmere in midweek.