The former Manchester United man was unable to complete the club's last match against Aston Villa, which ended 1-1, and will be out for another few weeks as he seeks a full recovery from the problem.
Summer midfield signing Vurnon Anita dropped back into Simpson's regular right-back slot and performed admirably in that game but youngster James Tavernier is also in contention for the role having featured heavily in pre-season and Newcastle's Europe League qualifiers.
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"It may be young Tav, who has been around the first team for a while now and has shown in pre-season what he can do. Sometimes you need a chance like this to step in and try to do a good job.
"Or it could be Vurnon, who has been playing in central midfield but can do a job at right-back and left-back as well. He's come in and slotted in straight away wherever he has played.
"With all the games we've got coming up, with the Europa League on top of everything else, it's good that we've got players who are quite versatile."