Westwood has been linked with Tottenham and Sunderland.
But Boothroyd insists he is yet to receive a single offer and believes the Republic of Ireland international will put pen to paper before too long.
"I met Keiren this week," the Sky Blues boss told the Coventry Telegraph. "I bumped into him and I expect him to sign. I want to keep him because he's a good goalkeeper."
He added: "We have not had one offer for him, not one, and the best place for Keiren is here at Coventry because it is all very well being a good player in a team that finishes mid-table, but to be a good player and international that contributes to a team that goes on to be a winning team is completely different.
"There is a time and a place for players to move and I think the game is full of players that move too early, but Keiren's time isn't now. He needs to stay here."