Wenger is keen to sign two players ahead of the World Cup, with Juanfran and Serge Aurier both identified as possible replacements for Manchester City-bound Bacary Sagna.
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"We want to win the Premier League and the Champions League," he is quoted as saying by The Times. "If we buy two or three players then I think we can.
"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."
Wenger broke the club's transfer record to sign Mesut Ozil from Real Madrid for €50 million last summer and Lord Harris believes "it would be easy" to top that this summer – as Arsenal can "buy most players" currently on the market.
"We would. It would be easy," he added. "I wouldn't say it [the total transfer budget] is £100 million, 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 [Lionel] Messi, [Cristiano] Ronaldo or [Gareth] Bale, we could buy most players."