The Dutchman believes that the Scottish Premiership title should not be at the top of the Hoops' list of priorities.
Former Celtic striker Jan Vennegoor of Hesselink has perhaps surprisingly claimed that Brendan Rodgers' main priority during his first season at Parkhead should be to try and make an impression in the Champions League, rather than retaining their Scottish Premiership title, The Scottish Sun reports.
Although Ronny Deila's tenure saw the Hoops win the league title in both of the campaigns he was in charge for, their inability to have any impact in Europe meant that he left the club with his spell being largely considered a mixed one.
And Hesselink has suggested that doing well in Europe has now got to be Rodgers' biggest priority, rather than concentrating on a sixth league crown in a row.
"People expected a big name and they got one, so it will be up to him to produce a team capable of getting into the Champions League," he told The Scottish Sun.
"That has to be the main aim, everyone knows Celtic will be going for the title in Scotland but getting to the Champions League is the main thing."
Doing well in the Champions League may well ultimately help the Northern Irishman attract higher quality players to the club in the future.
And with Rangers preparing for their first season back in the top flight, this upcoming season may therefore be the best opportunity for Rodgers to give Europe the kind of attention that will benefit the side in the future both domestically and on the continent, as they should have enough in the squad to see off any potential challenge in the top flight.