Nakamura has hinted that he could be looking to leave the club in January and return to his homeland, citing the travelling difficulties, but Strachan said: "He's got a strong mind and nothing upsets him so Naka won't complain.
"When the time comes, I'll understand why he wants to go back to his own country and play for his favourite team there.
"But Naka loves it here and he's made Scottish football more enjoyable.
"He's the best I've worked with and when he walks away I'll be on bended knee and thanking him because he's terrific.
"If I'm lucky to be here in 25 or 30 years' time I will still be thinking about Shunsuke Nakamura.
"It's not a love affair, it's just that I still remember playing with great players like Bryan Robson, Gary McAllister, Graeme Souness and Kenny Dalglish."
Strachan, a former Scotland international who spent a career facing players bigger and stronger than himself, hailed a kindred spirit in Nakamura.
He said: "He will go down as the most-kicked player in the SPL by a million miles and nothing fazes him."
Of the exhausting long-distance trips Nakamura continues to undertake, the Celtic boss continued along the same lines.
He said: "He is used to that journey now. (Australia international) Scott McDonald told me that the more times you do it, you more you get used to it.
"When you miss it for seven or eight months and then do the journey, it seems to be a problem."