A decision is expected to be made this week, traders said.
A trader at a foreign bank in Tokyo said investors were also speculating that Japan Exchange Group Inc, formed from the merger of the Tokyo Stock Exchange and the Osaka Securities Exchange in January, would join the Nikkei 225 constituent.
Japan Exchange Group, which has a market capitalisation of about $4.7 billion, advanced 1.4 percent to 8,600 yen, adding to a 9.1 percent rally on Monday.
Nintendo, which has a market capitalisation of $16.3 billion, has risen 29 percent so far this year, slightly underperforming a 33 percent rise in the Nikkei.