Last week, European soccer's governing body UEFA said that Euro 2020 will be held in 13 cities across the continent rather than one or two countries in a radical departure from the traditional format for major tournaments.
"In general, all games must be played at 50,000-capacity stadiums or at bigger ones," Mihaylov, who is also a UEFA Executive Committee member, told local media on Monday.
"UEFA will make only two exceptions and give two cities, which have stadiums with smaller capacity, the chance to host matches. This will be done to give smaller countries like Bulgaria an opportunity to host a match in the group stage."
Bulgaria's Vasil Levski national stadium, located in the centre of capital Sofia, has 43,230 seats but needs to be renovated to meet criteria set by UEFA.
Last year, the 53-year-old Borisov, who is still playing for third division team Vitosha Bistritsa, said the government was planning to construct several new stadiums if soccer authorities manage to attract fans back to grounds.
"The most important thing now is to talk to Prime Minister Boiko Borisov in the coming days about the government's intentions and whether it wants to participate in the construction of a stadium that meets the criteria set by UEFA," said Mihaylov.
"If we reach an agreement, we can bid to host one or two matches," he remarked, adding that UEFA will officially announce its requirements at March's Executive Committee meeting in Sofia.
"I believe that the prime minister, who is a sports person and does a lot for sport and football in particular, will support us."
According to media reports, Bulgaria's neighbour Romania is also interested in hosting matches at Euro 2020 though local soccer authorities have not confirmed the stories.
In 2011, Bulgaria and Romania considered a joint bid for Euro 2020.
Yugoslavia, which collapsed in the early 1990s, is the only Balkan country to have ever hosted a European championship finals. In 1976, the final four-team tournament was held in Belgrade and Zagreb.
Last week, the Serbian FA secretary general said Belgrade is hoping to host a game in 2020.
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