The Red Devils are leading contenders to end up as runners up behind Premier League champions Chelsea FC.
Manchester United are three points ahead of their bitter rivals Liverpool FC in the race to secure second spot.
The 20-time English champions will welcome Arsene Wenger and his Arsenal side to Old Trafford for the last time after the Frenchman announced last week that he would be standing down at the end of the 2017-18 season.
Manchester United have won five of their last six Premier League games but the Red Devils did suffer a surprise 1-0 loss to West Bromwich Albion in their last home fixture at Old Trafford.
Former Liverpool FC defender Lawrenson is backing the Manchester outfit to finish as runners up thanks in part to a comfortable win over Arsenal at Old Trafford on Sunday evening.
“United are looking very good for second place now – it is in their hands and with games against Brighton, West Ham and Watford to come after this one [v Arsenal], I don’t see them letting it slip,” Lawrenson told BBC Sport.
Liverpool FC are in the Champions League semi-finals and were 5-1 winners against AS Roma in the first leg at Anfield mid-week.
Manchester United suffered a surprise 2-1 aggregate loss to La Liga side Sevilla in the round of 16.
The Red Devils signed Alexis Sanchez in the January transfer window.
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