The greatest swimmer of all-time wants Tiger Woods to become the greatest golfer of all-time ... 'cause Michael Phelps tells TMZ Sports he wants TW to catch Jack Nicklaus' majors record!!!
"I hope he gets to 18," Phelps says ... "I'll say that."
Of course, Phelps famously had a front-row seat to watch Tiger's historic 15th major win at the Masters this past weekend -- which left Tiger just 3 short of Nicklaus' 18 mark.
Michael Phelps is all of us right now pic.