Rashford, 27, looks set to be announced as a Barcelona player imminently after reportedly signing the contract that would see him move to the La Liga champions on loan from Man United.
The England international made it known he wanted a “new challenge” after Amorim dropped him for the Manchester derby last December.
Lineker, who is the last Englishman to wear the famous Barcelona colours, believes Rashford will be a success at the club.
"He (Rashford) will do great. He seems to be in the right frame of mind," he told Sky Sports. "I think this is a great challenge. They have got brilliant players. They are a tough team. But there are so many games they are playing."
He then questioned the culture at Man United, pointing out that several players have gone on to succeed after leaving the club.
"Let's look at the players who have left Manchester United. They have done unbelievably well, everywhere," he said.
"So, there is something wrong at Manchester United. The players who have got away from there have generally succeeded. At Villa, he was terrific. And he can do the same sort of thing at Barcelona. I hope so."