Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
Arsenal captain Thomas Vermaelen has refused to talk about his future at the club.
Teenagers Crawford, 18, and Shankland, 17, and 22-year-old Sinclair will all travel to England on Monday and will stay until Thursday.
Ayr, who are a part-time club, confirmed that the trio would be due back by next Saturday ahead of their game at Brechin City.
Honest Men boss Mark Roberts told the Ayrshire Post: "We've also had clubs such as Bolton, Crystal Palace and Charlton at our games this season and it underlines that the Academy is doing a great job.
"Crawford and Sinclair are there on merit while Shankland is going due to his reputation since a boy.
"It's a great chance to train and learn. They are all aged under 23 so if anything comes from it, there could be good money for Ayr."