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Cooper, 47, was confirmed as Jamie Fullarton's replacement on Sunday, with the Scot having lasted just 70 days.
Fullarton's sacking came at the end of a spell that has seen a public row with Aborah, fans' protests and owner Ray Trew putting the club up for sale.
"It's time to come together," Cooper told BBC Radio Nottingham.
"We need everybody behind the club and the players to make sure it is a really good end to the season.
"I have had a chat with Stan. On both parts maybe the situation could have been dealt with differently. But I want to put as many good players as I can in the team.
"Stan comes into the reckoning as much as anybody. He is a good footballer and if he can help then he will play."
Cooper, the third Notts manager this season after Ricardo Moniz and Fullarton, takes over with the club on 40 points, 13 above the relegation zone with 10 games remaining.
But he played down the talk of achieving a set points total that will guarantee him continuing as manager when his initial contract expires at the end of the season.
"It's not as cast-iron as that," Cooper said. "It will be a case of me looking at the club and the chairman can have a look at me and we will see what we do at the end of season.
"If we can bring some stability and unity to the playing staff, the club and the supporters, then the future will be bright.
"The players were very receptive to what we are trying to put in place. We are trying to take the reins off them and give them a bit of a freedom.
"It's a fresh start and sometimes a new broom sweeps clean."
You can see Mark Cooper's first interview as Notts manager at BBC Radio Nottingham's Facebook page.
New manager Mark Cooper has called for unity at Notts County and has said out-of-favour midfielder Stanley Aborah has a future at the ailing League Two side.