Arsenal face stern competition for a top four place this season and Collymore is questioning the Frenchman's hunger to compete.
The upcoming Premier League campaign is looking likely to be a highly competitive one to say the least, with a number of new managers keen to make their mark.
Jose Mourinho and Pep Guardiola are looking to turn both Manchester sides back into powerhouses, while Antonio Conte has been brought in at Chelsea to help them bounce back.
Elsewhere, Ronald Koeman is looking to start a new era at Everton, while the likes of Mauricio Pochettino and Jurgen Klopp are looking to continue fine work at Tottenham Hotspur and Liverpool respectively.
There is also champions Leicester City to consider, and Collymore says he questions if Wenger has the hunger that those managers all have.
“If I was an Arsenal fan going into this season of the super manage then the one question I’d be asking is ‘Does our boss have the same hunger as the rest of those guys?” he told the Mirror.
“The answer would have to be no. That’s why Wenger needs those one or two "wow" signings and fast – otherwise Guardiola, Mourinho and Conte could taint his legacy for ever.”
It now remains to be seen if Wenger can secure those statement signings his team is crying out for.
So far Granit Xhaka has been the only major arrival, which is unacceptable to some given the strengthening their main rivals have done.
If he does not make such signings, it is easy to see Arsenal being left behind as Collymore suggests.