The coaches have been rivals in their respective positions with Barcelona and Real Madrid, but have been given a chance to share a studio with one another
According to El Confidencial, the pair was offered 1.5 million euros apiece to accept punditry roles with the Mexican multimedia company Televisa for this summer's tournament in Poland and Ukraine.
Guardiola, though, is rumored to have already said no, as he intends to honor his promise to take a complete break from the game after parting ways with Barcelona at the end of the season.
Mourinho, though, is believed to still be considering the offer. The Portuguese intends to play an active role in Real Madrid's player recruitment program for next season but is understood to be open to the idea of making himself available to Televisa for some - but not all - of Euro 2012.
Televisa has a history of hiring big names to cover major international tournaments, having used Luis Figo and Zinedine Zidane for its coverage of the 2010 World Cup in South Africa.