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The trio should soon be back in action following comments the club’s head of medical services Rob Price gave to Hull’s official website.
McGregor has been deemed “available for selection” while Price suggested that both Jelavic and Dawson should be back for Hull’s next match against Tottenham Hotspur later this month.
Hull slipped to 15th in the Premier League table after losing 1-0 to Burnley at the weekend and the centre-back has promised an improvement following the international fixtures.
“We know we are going to be better than that and we’ve got a lot to prove to the fans again,” he said.
Hull follow up that Tottenham match with games against Manchester United and Everton, so Steve Bruce’s side will have to be at their best to take much from those three encounters.