Hamilton’s junior career was supported by McLaren, and he drove for the team in F1 from 2007-2012 before leaving for Mercedes.
Though Alonso and Hamilton’s time as McLaren team-mates in 2007 was famously tempestuous, their relationship has improved.
The pair battled for ninth at the end of this year’s Mexican Grand Prix as Hamilton recovered from first-lap damage, and the 2017 world champion wants more of that next season.
“I had a great battle with Fernando earlier this year, towards the end of this season,” said Hamilton.
“I’d love to have more battles with him on a much more level playing ground.
“They’ve had such a difficult time. Given that I grew up with McLaren from 13, I go through qualifying and I always look to see where Fernando is, I always look to see where they are and am watching their progress.
“There’s just a natural place in my heart for them, because I achieved a huge amount with them. “I really, really hope next year is a successful year for them, I really hope we are battling with them because McLaren deserve to be at the front.
“I hope with this new power unit they’re there with us.
“I hope we have another incredible world champion up there with us fighting for the world championship.”