The Scottish champions are looking to defend their 2-1 lead from the first game at Parkhead last week. The Parkhead skipper's hip injury kept him out of the 1-0 SPL win over Aberdeen at weekend.
Mjallby said: "The Scott I know, I think the (chances of playing) are quite good - very good."
Winger James Forrest, who also missed the league's curtain raiser, is battling to recover from a groin injury but forward Georgios Samaras has shrugged off the effects of a face injury sustained against the Dons while defender Charlie Mulgrew returns from suspension.
Before flying out from Glasgow airport, Mjallby said "Everyone is travelling except for Mo Bangura who has a thigh strain.
"We have to assess a few of the boys after training tonight. They (Brown and Forrest) missed out on the game at the weekend but we are delighted they are with us now.
"Obviously the physios and the doctors will do their best to make sure they are available for selection."
The former Celtic defender added: "We are leading 2-1 and yes, we are playing away from home but I don't see any reason why we can't go over there and win.
"But we need to be solid, we can't make the same mistake we did a week ago when we conceded a goal on the counter-attack.
"I think Helsinki will need to go forward more than they did at Celtic Park which hopefully means there will be more space for our attacking players."
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