The Gunners are set to be busy in the summer transfer window, with the confirmation of the free transfer of France Under-21 attacker Yaya Sanogo set to be shortly confirmed now his contract with Auxerre has expired.
Additional funds of more than £75million are understood to be available for manager Arsene Wenger as he aims to pull together a squad capable of mounting a long overdue sustained assault on the championship.
Rooney asked to leave Manchester United at the end of last season but it remains to be seen how the situation will develop with the arrival of new manager David Moyes, his former boss at Everton.
Wilshere, though, would welcome his fellow England international into the Emirates Stadium dressing room.
Speaking in a question and answer session with espnfc.com, Wilshere said: "If it happens, it would be amazing.
"He (Rooney) is the type of player who can win you trophies - and just to see his name on the team sheet brings fear to the opposition. We could do with a little more of that."
Arsenal have also been linked with Real Madrid's £25million-rated forward Gonzalo Higuain and also Everton midfielder Marouane Fellaini, who would, like Rooney, both command significant wages.
Wilshere, 21, believes the calibre of players now likely to be brought in by Arsenal shows they mean business on the pitch.
He added: "You look at the type of players like Higuain we are trying to bring in and you have got to be encouraged.
"I think we need a few more, not to step right into the team, but to add to the squad.
"We need our squad to be as deep as United's and (Manchester) City's. They can change their back four completely and still win. There is no way United would have won the Premier League trophy with 18 players."
Wilshere added: "It is no secret we need to win a trophy. How long has it been now, seven or eight years?
"The players feel the pressure and we have gotten close a few times like with the Carling Cup a couple of years ago.
"I think once we win one, others will follow."
Arsenal have already confirmed Andrey Arshavin, Denilson and Sebastien Squillaci will leave once their contracts expire and more funds will be freed up by the departure of other fringe players such as Denmark striker Nicklas Bendtner, Swiss defender Johan Djourou and Morocco forward Marouane Chamakh.
Wilshere saw his own progress last season hampered by a series of niggling injuries, but fees the ankle is now "100 per cent" as he prepares for Arsenal's tour to Asia.
"I am really looking forward to having a solid pre-season. I haven't had one in two years and once you miss it, you are always playing catch-up," he said.
"It's a chance to show the manager that you deserve to be in the team and I think there's going to be competition for a few spots, but that's a good thing.
"If you're going to challenge for trophies, you need a big squad. You can't expect 11 players to do it every week."
After a superb 10-match unbeaten Premier League run saw Arsenal finish fourth and secure a place in the Champions League qualifiers, hopes are high that next season can finally bring Wenger's men a first piece of silverware since the 2005 FA Cup.
German forward Lukas Podolski is confident the Gunners can hit the ground running.
"(The hopes are) very big. Firstly, I am happy, but I believe that the second season will be even better," Podolski said on Polish news site gwizdek24.pl.
"If we take the (Premier League) table for the last 15 games, then Arsenal would be first or second.
"Now the question is, can we be in such form throughout the season?"