More than £800,000 has been raised by the share issue scheme launched in October and although that is short of the £1.79million target and a £1m shortfall could result, immediate fears have been allayed.
Director Sergejus Fedotovas has warned of tough times ahead, but McGlynn remains optimistic of on-field success.
Eighth-placed Hearts responded from the loss at Hibernian which saw them fall at the first hurdle in defence of the William Hill Scottish Cup with a 2-0 defeat of Aberdeen and McGlynn now hopes for another victory at St Johnstone on Saturday.
"If we can win on Saturday against St Johnstone we would go above them on goal difference and be in a very positive position," he said.
"We've got a semi-final of the league cup to look forward to in January. That would be a big plus for us, and we still believe we can finish as high as any of the other teams (in the league).
"We're still not that far away from teams that have been going on 10-game unbeaten runs and all the rest of it.
"We've picked up enough points to be within two or three victories of these teams and I believe we can do that."