Wenger broke the club's transfer record last August when he signed midfielder Mesut Ozil from Real Madrid for £42m.
Lord Harris is adamant Arsenal remain ambition to challenge for the top honours, and he claims there are very few players the club would not be able to afford.
"We want to win the Premier League and the Champions League. If we buy two or three players then I think we can," Lord Harris said in the London Evening Standard.
"We want to win. We don't want to be second, we don't want to be third and we don't want to be fourth.
"We will support Arsene with the players he wants to buy. He has always been encouraged to spend."
Arsenal have been linked with former midfielder Cesc Fabregas, who is apparently surplus to requirements at Barcelona.
Real Sociedad winger Antoine Griezmann is another reported target, while Toulouse right-back Serge Aurier is an option should out-of-contract Bacary Sagna leave.
Lord Harris reckons only Barcelona talisman Lionel Messi, and Real Madrid duo Cristiano Ronaldo and Gareth Bale would be out of Arsenal's reach this summer.
Although Lord Harris refused to divulge the budget available to Wenger, he did confirm the club would be willing to allow Wenger to once more break the club's transfer record.
"We would. It would be easy," Lord Harris said. "There is a lot of paper talk. I wouldn't say it is £100m, I wouldn't say it's £50m and I wouldn't say it's £150m.
"If Arsene has asked for any player then we have always backed him to go and buy. With the exception of Messi, Ronaldo or Bale, we could buy most players."