Dish Network has offered $5.5 billion more that Japanese operator Softbank for a majority 70% in Sprint, which it had agreed terms for last year.
Speaking at a company earnings briefing, Son said "there is absolutely no need" to increase its $20.1 billion bid as it holds better value.
Softbank is looking outside of its domestic market as it faces competition from NTT and KDDI in Japan and started preliminary talks with Sprint in October 2012 over a deal.
The Japanese operator is looking to roll out a high-speed network to compete with Verizon and AT&T's network, if a deal were to go ahead.
Sprint CEO Daniel Hesse said the company has set a date for potential deals to be finalised.
Hesse said: "We're buying more spectrum from a company called US Cellular, we're buying Clearwire and then there's the SoftBank investment into Sprint."
"We're working to get all three of those finished and closed by the first of July. We have a special committee of the board that in parallel will evaluate the Dish proposal."
Intel chief executive Paul Otellini has also backed Softbank's bid in a letter addressed to outgoing FCC chairman Julius Genachowski.
"We need this competition in the wireless space as the AT&T and Verizon model is not giving that to consumers at this time," Otellini said.
An Intel spokesman told Reuters that Softbank is a "market disrupter".
