I'm the manager for arsenal, and I've been trying to buy Rooney. However it says Man Utd are "too cautious" to even look at my offer? Is it because of the whole rival thing and will I ever succeed in getting Rooney while he is on Man Utd?

It's probably because you are a rival. I don't think it's possible to get him, unless you break the bank.

The best thing to do here would be to transfer you players from Utd to the Gunners before you start season mode. If you dont want to do that hen just transfer him to another non rival team and buy him in manager mode. Another alternatively would be to manage a non rival team in the first season, buy Rooney and then manage arsenal in your second season and buy him from the previous tea. If you dont want to start a new manager mode then just wait for his contract to run out and buy him as a free agent