Hamilton, who drove alongside Button at McLaren for three years, said: "I hope Jenson comes back".
"On the planes, I will try and look at some videos and races from past years and try to learn as quick as I can", said Alonso.
"No, it (Indy) is a single race", said the Spaniard, after he and McLaren-Honda shocked the racing world on Wednesday by announcing they will contest the Indy 500 next month.
Button, who drove for McLaren from 2010-16 and has been retained by them on a sabbatical, is the No1 candidate to replace him at Monaco, although the 37-year-old former world champion has yet to drive the team's 2017 vehicle. "His auto is going to run with some guy everybody will be pretty familiar with".
The team were expected to make big leaps up the order this season after finishing sixth overall a year ago.
But Brown denied suggestions allowing Alonso to race in Indianapolis is a ploy to keep him around for the 2018 campaign.
"But at the same time I think it's a great challenge for Fernando". "It will be hard if we can't". "I need to learn many procedures, like the restart, the pit stop sequences, many things that will be new for me, apart from obviously the auto and racing on the ovals that definitely is a big challenge".
Alonso went on to say the Indy 500 would not have even been a consideration if Honda's 2017 Formula One engine had lived up to expectations. Alonso makes sense now that McLaren is run by Zak Brown, who ran an Indianapolis-based marketing firm for years before his gradual move into Formula One.
"I'll be flying to Indianapolis from Barcelona immediately after the Spanish Grand Prix, practising our McLaren-Honda-Andretti vehicle at Indy from 15 May onwards, hopefully clocking up a large number of miles every day, and I know how good the Andretti Autosport guys are", Alonso told BBC.
Mr. Button has "temporarily" retired from Formula 1 at the end of last year's season, but he only did that to focus on his passion, which appears to be running in Ironman triathlons.
"But it is cool that he is doing it, I think personally he has picked a very good time to do it".
McLarens won the Indy 500 three times in the 1970s, initially with Mark Donohue in a Penske-run chassis, then as a team in '74 and '76 with Johnny Rutherford.
McLaren do have 2009 champion and former Monaco victor Jenson Button as a potential stand-in, however, even if nothing has been confirmed, with the Briton technically only on sabbatical.
"If I want to be the best driver in the world I can either win eight F1 World titles, one more than Michael, which is impossible".
"We know with the package we have in the last couple of years, we have the best opportunity and we achieve the best results".