Koeman is making a big impression after a summer move to Everton, with his side's 3-1 win against Middlesbrough on Saturday evening firing the Toffees up to second spot in the fledgling Premier League standings.
"If I was Arsenal and Wenger is ready to go, Koeman would be the number one target for me," Nicholas told Sky Sports.
"There's a shrewdness about Koeman - he doesn't complicate himself. Once he's made his decision it's all in. I just love his whole approach."
Despite their impressive start to the season under Koeman, Nicholas does not expect Everton to mount a sustained push for the Premier League title.
"I don't think they are title contenders, but I've been very impressed," he added.