The likes of Manchester United and Manchester City have been spending in excess of £150m for the last couple of years, while Premier League champions Chelsea and even Liverpool made a decision to splash the cash over the summer.
"We did that for 20 years".
"He's getting stronger every day and that's what I want from him".
"For a striker it's always important to score, the statistics are very important, and I keep it in a part of my mind, but the most important thing for me is to win and after that the goals will come", he said.
Wenger has included Chile forward Sanchez in his squad for Thursday's game.
The competition could, possibly, also provide the Gunners with an alternative route into next season's Champions League, an opportunity that Manchester United took up with aplomb last term.
Following their 3-0 win over Bournemouth at the weekend, the Gunners will be heavy favourites going into the match.
The England midfielder was linked with a move away from The Emirates Stadium last summer, with Turkish club Trabzonspor revealing this week they held talks with Wilshere over a loan move.
With Cech out, David Ospina is likely to start in goal, Per Mertesacker can expect to start in defence, Jack Wilshere seems nearly certain to be handed a role in midfield, while Theo Walcott, Alex Iwobi and Olivier Giroud will be vying for roles in the front three.
Alexandre Lacazette scored his second league goal of the season, with Danny Welbeck adding a brace.
"It's true that I was close to leaving the club because I said that I wanted to play", he said. Thursday to Sunday morning is short so I have to think about that.
Though the visit of Cologne is the next challenging facing Wenger and Arsenal, the trip to Chelsea on Sunday [17 September] looms large.
A good guess is that Wenger mimics his tactics from previous early FA Cup rounds, when he usually plays a number of his first-team backups along with one or two academy prospects.
"We will take it seriously but the priority is to focus on the Premier League and combining the two", said Wenger.