The 24-year-old utility man put in a man of the match display in the 1-0 win against Watford at the Emirates last week after returning to the starting XI.
Campbell, who won the First Division title with Arsenal in 1991, has claimed that Maitland-Niles could be in line to be rewarded with a new contract in the future.
His current deal in North London expires in 2023.
Speaking to Football Insider, Campbell said: "A new contract is a definite possibility.
“Every time Maitland-Niles comes into the team now he looks focused. There have been no lapses in his performances. He has done the job.
“I was very impressed with him on Sunday. There were two or three players who could have got man of the match and he was one of them. He was brilliant.
“It was a new partnership in midfield to start the game. Both Maitland-Niles and Lokonga did really well.
“Maitland-Niles has great energy and he can play. I hope it continues. We need as many home-grown players at the club as possible."
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