"I will do a little bit for the game, not for money but for enjoyment," Muralitharan told the Mumbai-based Daily News and Analysis (DNA) newspaper.
"I've already spoken to Anil and we will try and get together and do some coaching in the spin department.
"He is one of the greatest bowlers I have seen and he knows a lot. We will see which country needs help. We are looking at subcontinent countries and academies."
The Sri Lankan off-spinner is the world's leading bowler in Tests with 735 wickets in 120 matches. He is followed by retired Australian Shane Warne (708) and leg-spinner Kumble (608).
Murali is also the second-highest wicket-taker in one-day internationals with 464 scalps in 305 games after retired Pakistani fast bowler Wasim Akram (502).
Coaching bowling is not about technique but about how to use the conditions, he said.
"When both of us call it a day we will look at coaching together. Hopefully, it will help future generations," he added.
Muralitharan said his twin objectives were to reach 800 Test wickets and surpass Akram's one-day record.
"I am targeting 800 Test wickets. If I get that I will be very happy. Then I will try for a few more wickets in one-dayers to get the world record of Akram. When it is done there is nothing more to achieve for me," he said.
When asked whether he would call it a day after achieving these aims, he said: "I think so. Looking ahead there is no future because if some bowlers are coming through in Sri Lanka I would like to give them a chance.
"I can achieve 1,000 Test wickets, but the thing is it is too long and too hard to achieve. I am 36 now and you have to retire when you are on the top. Numbers are going to be just numbers for your own satisfaction."
Muralitharan's bowling action has been questioned during his illustrious career, but the ace spinner said he has never allowed the controversies to affect his performance.
"You don't want to give up just because of what some people say. You want to prove yourself. That is the way I look at life," said Muralitharan, who was called for throwing on Australian tours in the 1990s.
"I want to go forward instead of taking a backward step. I knew that I had the talent to go forward. So anyone trying to stop me, they tried their best, but couldn't."