However, contrary to Japanese reports, City have yet to make an offer to sign the Asian Youth Player of the year.
The teenager has shone in recent months and has been key to Shimizu's march to the Nabisco Cup final on Saturday, as well as their late surge in the league.
Although Shimizu team manager Afshin Ghotbi wants to keep the 18-year-old within his ranks, he is also keen to give Ishige experience of a spell at City.
"If you want to build top-class players, you have to give them various experiences and opportunities to see first-hand what the world level is about," Ghotbi said.
"And what better experience for Ishige than to train with the first team of Manchester City, the champions of England, and have (manager Roberto) Mancini see him first hand and train with some of the top players in the world," he told Japan's Kyodo News.
Ishige is set to spend time with City in January.
The former Iranian national coach said other European clubs were also keen on the teenager.
"There is interest in him, not just Man City but many clubs in Europe and he deserves it. He's a real fantastic talent," Ghotbi said.
"As far as I'm concerned, he's not for sale and we want him to be a part of S-Pulse for the next few years to come. There has been no offer, (City) just want to see him and we are doing the same with other players with other clubs.
"The greatest asset of Japan is its youths. I'm very, very positive about the youth players in Japan and their qualities. Ishige is a perfect example of what I'm talking about."