Arsenal are determined to improve the side ahead of next season to mount a long-overdue assault on the Barclays Premier League title, and chief executive Ivan Gazidis has talked about "an escalation in (the club's) financial firepower" that would allow them to move for a stellar signing.
However, Robson, who came through the Arsenal youth system but left Highbury in 1986, long before Wenger's arrival, feels some of the manager's recent transfer dealings should not inspire much hope for the calibre of player who will arrive at the Emirates Stadium ahead of next season.
Speaking to talkSPORT, Robson said: "I am not expecting any marquee signings at Arsenal. There is a lot of talk about it, but I don't know if I would trust Arsene Wenger with that money.
"Over the last few years some of the players that he has said were going to be world class haven't ended up like that - people like Philippe Senderos, Denilson, Marouane Chamakh, Armand Traore, Sebastien Squillaci, Nicklas Bendtner, Carlos Vela, Emmanuel Eboue, Park Chu-young, Lukasz Fabianski, Gervinho and Andre Santos.
"Over the last two seasons they have spent some money on Olivier Giroud, Lukas Podolski, Mikel Arteta, Nacho Monreal, Per Mertesacker and Andre Santos. They haven't been top-class players.
"Arsene Wenger doesn't appear to want to sign the top-class players, or what other people would describe as top-class players.
"He goes out and says: 'I can buy you cheaper players for a better price who are going to be world-class players in the future', but that hasn't been the case in the last few years.
"Some of the players who he has bought have regressed under him like Andrey Arshavin and Thomas Vermaelen. Nacho Monreal hasn't been a good signing and Andre Santos has been hopeless for them.
"Per Mertesacker and Lukas Podolski are past their best and Gervinho is another player who they spent a lot of money on and hasn't really come to the fore."
Arsenal's wage bill of some £143millon was around 61 per cent of their overall revenue but is set to be reduced this summer by the confirmed expected departures of Arshavin, Denilson and Squillaci, while several other surplus fringe players should also be offloaded - such as Chamakh, Bendtner and Korean forward Park.
Wenger has already begun his summer rebuilding plans, pushing through a deal for France Under-21 forward Yaya Sanogo, on a free from Auxerre, and Arsenal are said to be tracking several other high-calibre reinforcements in the Premier League and across Europe.