The Tottenham winger has been in fine form this season and has netted three goals in three games for club and country in recent weeks.
The 23-year-old is understood to be a top target for Real Madrid following his impressive form over the last couple of seasons.
And fellow Welshman Earnshaw believes the former Southampton player should try and secure a transfer to Spain in the coming seasons as he continues to develop.
“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.”