The country voluntarily withdrew from hosting test matches in January 2006 but have in the past year staged one-day games with Ireland, Sri Lanka and India.
"We're still not sure if they'll be including tests this year," the source told Reuters on Thursday.
A spokesman for governing body, the International Cricket Council (ICC), said it had not barred the country from hosting test matches and had done everything possible to facilitate its return in staging the five-day international form of the game.
Zimbabwe lost their first match in the 50-over World Cup on Monday, falling by 91 runs to holders Australia in Ahmedabad.
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