The former Newcastle star is currently training with the non-league club after being invited along by Bruce, the club's new manager.
He joins former Everton and Hull star Oumar Niasse in training with the Northern Premier League side.
Cisse, now 38, has been without a club since leaving French Ligue 2 side Amiens last summer.
Having scored 12 times for the French outfit last term, Cisse would be a major coup if he was to join Macclesfield, particularly after scoring 44 times for Newcastle in five years at the club.
Speaking on The Sports Breakfast, Bruce said: "We all live in Cheshire so it's a catchment area and there's a lot of footballers around and I got a call from Stephen Ireland, believe it or not, who organises, shall we say, a retirement squad who play every Tuesday night, nine-a-side.
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"We've played for about a year and a half now with the likes of Joleon Lescott, Papiss, Oumar Niasse, Stevie [Ireland], Phil Bardsley, Antonio Valencia - the list goes on!
"So we all rock up on a Tuesday and play nine-a-side and I have to say, Oumar Niase and Papiss [Cisse] still look the part, so I said to them 'I've just got the Macclesfield job, do you want to come and train, raise the standard and see if you enjoy it' and that's what they did last week and that's where it's come from."
"We just got the job a couple of weeks ago and I just thought if we could get a couple of older pros in and show the quality that they bring - that's exactly what happened. The quality that they brought to the session was great, they had a good runaround.
"I think they needed a bit of WD-40 afterwards, but other than that they were alright!"
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Speaking about his decision to take charge of Macclesfield, Bruce explained: "It's a project. I knew that when I went in I needed an opportunity and needed a project and I'm fortunate that Robbie Savage and Rob Smethurst, the owners, have given me that.
"They've obviously had bad times, Macclesfield, and had to drop to the bottom of the football pyramid and have been back at it for a couple of years.
"They want to get back into the Football League and I just thought that it was a project that I fancied getting my teeth stuck into."
Asked about the influence of his father, Steve Bruce, Alex added: "I've been brought up with the game.
"I've had ringside seats to what management is and I always wanted to have a crack at it and I've got the opportunity to do that now.
"If I'm in it for the long-haul you'll have ups and downs, but we'll just have to see how it goes.
"As long as I don't start looking like him, I'll be alright!"