The Red Devils were held to a 2-2 draw with Southampton at St Mary’s on Saturday evening after Manchester United came from 2-0 down to rescue a point.
Mourinho’s side managed to go four games unbeaten before a 3-1 loss to defending Premier League champions Manchester City in the derby at The Etihad.
Manchester United were held to a 0-0 draw with Crystal Palace at Old Trafford last month before their stalemate on the south coast last weekend.
Arsenal, on the other hand, have made strides forward under Arsene Wenger’s replacement Unai Emery to lay down a marker in the top-four race.
The Gunners were 4-2 winners against Tottenham Hotspur at The Emirates on Sunday afternoon after Arsenal displayed character to overturn a 2-1 deficit to secure three points.
The north London side are unbeaten in their last 12 games in the Premier League to put themselves in the frame to challenge for a top-four finish.
However, former Liverpool FC defender Lawrenson believes Manchester United will secure a 2-1 win against Arsenal at Old Trafford on Wednesday night.
“Sunday’s north London derby was the perfect script for Arsenal, where they started well, found themselves 2-1 down but came back with a massive bang,” Lawrenson told BBC Sport.
“They would have probably beaten anybody with the way they played in the second half – they were that good.”
He added: “Manchester United dropped more points in their draw at Southampton, but it was not a huge surprise. It was the same old story in many ways, in that they did not play well but managed to get a result.
“Despite the contrast in both sides’ form, I still have a feeling United will find a way to win game.
“They need the three points if they are going to have any chance of making the top four by the end of the year, which is Jose Mourinho’s target.”
Arsenal lost to Manchester United at Old Trafford and The Emirates last season in Wenger’s final campaign in charge of the north London side.
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