Tottenham Hotspur winger Bale has been linked with moves to both La Liga giants in the past and fellow Welshman Earnshaw believes that a move to either club would help him develop further.
"Sometimes you just think that he can be unstoppable and he should, in the next year or so, move to Real Madrid or Barcelona," Earnshaw told talkSPORT.
"I want to see him at that level and I think that will take him on to a different stage again because he'll improve again.
"He's been at Tottenham for quite a while but sometimes it's nice to see people do well and go higher, and reach the top. There is no higher place than Real Madrid or Barcelona."
Bale has scored 13 goals in 28 appearances for Tottenham this season.