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Alonso is contesting his first Dakar this year as part of the Al Attiyah-led Toyota contingent, and sits 16th in the overall classification after the first half of the marathon.
Though a two-hour delay for repairs on the second day has knocked his chances at a headline result, the two-time Formula 1 champion has impressed his rally-raid regular rivals by producing bouts of frontrunning pace.
Al-Attiyah said Alonso caught his eye during the most recent stage on Friday, in which the Spaniard finished ahead of Al Attiyah's long-time Toyota Gazoo teammates Giniel de Villiers and Bernhard ten Brinke.
"A really good week," Al-Attiyah said of Alonso's performances. "Only one day that was really bad luck for him, but if you see the performance, really, today he surprised me - much better than Giniel, much better than ten Brinke.
"For a first Dakar... I know he's a really tough guy, he's learning. This is good because it means next year he will do Dakar."
Though the assertion was seemingly made somewhat in jest, Al-Attiyah subsequently reiterated his view of Alonso's return to the Dakar as being likely.
Asked if he expected Alonso to challenge for victory in 2021, Al-Attiyah said: "Winner? I don't know, you need to have time. You need to have really good experience.
"I am sure he will try, and if he finishes top three or top five will be good.
"We need him. I am sure he will bring more Formula 1 drivers, you know? Maybe Jenson Button, why not?
"I see him [Button] in Baja 1000 in Mexico and he did the race, and I think why not, he can do Dakar."
A fellow F1 champion, Button was Alonso's teammate at McLaren in 2015-16, before ending his full-time grand prix racing career.
He has since become a Super GT champion with Honda, but has no confirmed full-time racing plans in place for 2020.
Button contested the off-road Baja 1000 event in Morocco last month, and found himself stranded in the desert for 17 hours after a mechanical failure.
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