Alonso will skip the most iconic race on the Formula 1 calendar to race in Indianapolis, with Button – who remains contracted to McLaren – the favourite to replace the Spaniard.
"I hope Jenson comes back, it would be great for the sport to have Jenson back," said Hamilton, who was Button's team-mate at McLaren from 2010-12.
"I still think he is one of the best drivers, his calibre is very high, and he is experienced."
Button was replaced by Stoffel Vandoorne for the current season, but McLaren retain the option of promoting the 2009 world champion back into the cockpit in 2018.
The 37-year-old has done little to dampen speculation, tweeting “why do I have so many missed calls” after Alonso’s announcement.
Read the full article on eurosport.co.uk: Hamilton backing Button to replace Alonso in Monaco