Groves has already slammed his players for the passionless performance and admitted his job is on the line.
Furneaux however has gone on record saying that the board won't be sacking Groves, instead they'll be trying to help him.
I hope there's a reaction on Saturday. There are still 22 games to go as there was when Paul first came into the job two years ago," he told the Grimsby Telegraph.
"We need to be finding out where we go from here and find a way forward.
"We don't have panicky board meetings over things like this. I know the trend has not been good.
"We need to have a chat with Paul, which we would do in any case, to see if there is anything that we can do.
"We need to establish if there are problems that we can assist with from a board point of view.
"We're doing all we can to make the players comfortable - but we need to check if there are any underlying factors which we're not aware of that are contributing to the current form.
"From that conversation we'll listen to the manager. That's the way we work. We don't work by threats.
"Everybody has had a go at me this weekend but everybody in the club are disappointed with the run of form."
Has Groves got the dreaded vote of confidence from the board? It appears so.