The £15m man is excited at the prospect of the 18-year-old coming to Tyneside, even though they would be in direct competition for a place in the team.
"It would be fantastic to sign Wayne Rooney and I think it would be a good move for him," Shearer said.
"He is only 18 - if he wants to go to Real Madrid or anywhere in three or four years' time, he will only be 22.
"I think it will be a great investment for this football club, I really do. He is already one of the world's best, even at 18, and he can still come here and carry on to learn.
"It will be a great coup for Newcastle if we get him. We haven't got him yet, but it is great to see the club competing at the top end of the transfer market.
"Hopefully we can get him and the likes of him. If he chooses here over whichever options he has, then it will be great for us. I hope we get him, I really do."
Everton revealed they had rejected an improved bid from Newcastle and have done likewise with an offer from Manchester United, believed to be around the same £20m mark originally proposed by the North-East side.
Shearer's response to the interest in Rooney was in stark contrast to that of current sidekick Craig Bellamy, who said after Wednesday night's 2-2 draw with Norwich that he might have to consider his options should it materialise.
"You have to make exceptions for the likes of Wayne Rooney - because he is an exceptional talent - if he takes someone's place," the 33-year said.
"There are a lot of ifs and buts, but he will be a great asset for this football club.
"For me, I am excited at the prospect of him coming here, I really am. I was a touch surprised when I first heard we had gone in for him, but then I realised we were going for him and money talks. We will keep our fingers crossed he comes here."