It has emerged in the Bangladeshi media that the 27-year-old contacted coach Chandika Hathurusingha to tell him he was considering his future after the Bangladesh Cricket Board (BCB) asked him to return early from his participation in this year's Caribbean Premier League.
Seemingly irked by the request, Shakib - who has appeared in 34 Tests and 136 one-day internationals - reportedly spoke to Hathurusingha, who notified BCB president Nazmul Hasan via email.
Hasan expressed his disappointment at Shakib's threat, and underlined his intention to speak to the player to try and resolve the situation.
"I've received a letter in this regard," he told newspaper Prothom Alo.
"I cannot understand how he can make such a threat.
"I want to speak to them in person for details on the matter.
"If this is indeed true, nobody will be spared. There will be no compromise on discipline."
Hasan added that Shakib may well face sanctions for his actions.
"He has broken the discipline," he said. "We are very strict in this regard.
"The board will take a decision on giving him the NOC [No-Objection Certificate] in the July 7 meeting."