The manner of the defeat has raised questions over the future of the current Arsenal side, with striker Emmanuel Adebayor admitting in the aftermath of the defeat that the team was at a 'crossroads'.
Wenger has another year to run on his contract and Hill-Wood insists the Frenchman's future is not under scrutiny despite finishing a fourth successive season without a trophy.
"Arsene's future is not in question, although I am sure there will be people who have nothing better to do trying to suggest it is," Hill-Wood told the Daily Star.
"He has another season left on his contract and if he was to ask for an extension we would be delighted.
"But he hasn't discussed it with us and we haven't discussed it with him. There are other things to think about."
FundsHill-Wood also insisted the club will back Wenger in the transfer market this summer to improve the squad.
Wenger recently claimed financial restrictions had forced him to rely on his young stars this season, but Hill-Wood is adamant the Frenchman has not been denied substantial transfer funds.
Hill-Wood added: "That is not strictly correct. We have never denied Arsene any transfer requests.
"We spent a lot of money on Andrey Arshavin at the beginning of the year.
"And the money is there in the summer if he wants it. I'm not going to say how much though,because that would not be helpful to us."
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