The France international did not travel to Manchester City after making a series of critical comments about his team-mates while on international duty in midweek.
Speaking to the Sunday Mirror, Hill-Wood declared: "This issue has shown that Arsene can be ruthless. He has to be otherwise people can run all over you.
"As for whether Gallas has a future at the club, that will be up to Arsene. But I think Gallas has got a problem. Arsene will advise the board over that and we will support him no matter what.
"We will all be at The Emirates on Tuesday (for the Champions League fixture with Dynamo Kiev) and I am sure the matter will be discussed with Arsene. And 100 per cent we will endorse what he decides about Gallas."