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Real are also keeping tabs on Mbappe, who will be a free agent at the end of the season when his Paris Saint-Germain contract expires.
There has been speculation surrounding a blockbuster Real double swoop for Haaland and Mbappe as they look to snap up a couple of 'Galacticos'.
But Pique believes the Borussia Dortmund superstar shouldn't join the same side as Mbappe, citing the Ballon d'Or.
Speaking on Twitch via Football Espana, the Barca defender said: "If I were Haaland and I wanted to win the Ballon d’Or, I wouldn’t go to the same team as Mbappe."
Haaland's name continues to dominate the rumour mill, with both Spanish giants as well as Manchester City and Bayern Munich also thought to be monitoring his contract situation.
The Norway international expressed his frustration at Dortmund over his deal amid intense interest from Europe’s elite clubs.
"The last six months I have chosen not to say anything out of respect for Dortmund, but now the club has started to press me into making a decision," the 21-year-old told Jan Aage Fjortoft for Viaplay last month.
"All I want to do is play football. But they press me […] about my future, so that means I have to make a decision soon.”
When asked if he could decide imminently over his future, he added: "That is what they [Dortmund] want. It means things will happen now.
"They have started to put a lot of pressure on me, and I have to accept that […] so now is the time to get things started."