The Barbados and West Indies fast bowler is set to miss the County Championship Division 1 opener for Yorkshire against Warwickshire at Edgbaston.
But Martyn Moxon, Yorkshire’s director of professional cricket, is hoping that Best can ease the county’s problems by the end of a hectic April.
“We’re still waiting for Tino’s work permit to come, and I can’t see him being here for Friday, to be honest,” said Moxon in a newspaper interview.
“We’ll see how Tino goes this month and then make a decision really. From then, hopefully everything will be a bit clearer.”
Moxon added: “If [Tino] goes well, then that will make the decision a lot easier in terms of what we do for the rest of the summer.”
Best’s paperwork could be completed in time for him to make his debut for the county in the home clash with Somerset next week.
Yorkshire have only Tim Bresnan and Ajmal Shahzad to call upon, and they will only be available for the first two matches, after which they travel with England to the Twenty20 World Cup in the Caribbean.
Best came into the picture for Yorkshire, when he trialled with the club on their pre-season trip to Barbados.
This followed the unavailability of Australian all-rounder Ryan Harris, their first-choice overseas signing, and an injury to New Zealand replacement player Daryl Tuffey.
Harris is currently on Indian Premier League duty with Deccan Chargers, and Cricket Australia have ordered him to rest ahead of a hectic schedule for the national team, starting in June.
Yorkshire won just two matches out of 16 to finish a disappointing seventh in the County Championship last season.