The Red Devils head into the game looking to keep pace with Manchester City, who are in danger of moving completely out of sight at the top of the table.
Manchester United spent last week on a warm weather training camp in Dubai as they worked on their fitness levels ahead of the clash with the Potters.
Stoke are currently without a manager after the sacking of Mark Hughes earlier this month and former Liverpool FC star Lawrenson is not expecting Manchester United to have any problems against the Potters.
Speaking to BBC Sport, ex-Liverpool FC man Lawrenson said: “Stoke are still without a manager at the time of writing, and it will be very interesting to see who they appoint.
“Will it be someone to get them out of a mess, or are they looking for someone more long term?
“The tried and trusted managers that struggling clubs like Stoke might have turned to – the likes of Sam Allardyce and Tony Pulis – are all in jobs.
“And, if it is someone more long term, then he might not be able to keep them in the Premier League.
“Whoever is in charge, I don’t see them having any success at Old Trafford.
“Manchester United have started playing well and winning again – and I think that will continue on Monday.”
Manchester United are currently in second place and 15 points behind leaders Manchester City after 22 games of the new campaign.
The Red Devils have not won the Premier League title since their final triumph under Sir Alex Ferguson back in 2013.
Manchester United are currently preparing to take on Sevilla in the last 16 of the Champions League next month, after having won both the Europa League and League Cup under Jose Mourinho last season.
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