The FA has also been in touch with Greater Manchester Police with a view to ensuring the second leg passes off without incident.
Both clubs will be under huge scrutiny both before, during and after Wednesday's second-leg at Old Trafford.
In September, Neville was cautioned about his future conduct following United's dramatic 4-3 derby win in the Premier League when he ran towards City fans to celebrate Michael Owen's injury-time winner at Old Trafford.
The England defender received a £5,000 FA fine and was warned over his future conduct in 2006 because he celebrated in front of Liverpool's fans after United secured a late winner over their rivals.
Argentine Tevez joined City in July 2009 following an extended, two-season loan deal with United, with whom he won two Premier League titles and the Champions League.
His move to bitter rivals City angered United fans as Tevez was a firm favourite with Old Trafford supporters.
Before the first-leg tie at Eastlands, Neville said United manager Sir Alex Ferguson had been right to let Tevez leave the club last summer, rather than signing him on a permanent deal after his two-year loan spell ended.
Tevez scored twice in City's 2-1 win, and gestured and cupped his ears after scoring his second goal
Cameras appeared to catch Neville making an obscene gesture in response, and afterwards Tevez said his celebration had not been aimed at the United bench but specifically at his former team-mate.
"My celebration was directed at Gary Neville," Tevez told ESPN Argentina.
"He acted like a complete boot-licker when he said I wasn't worth £25m, just to suck up to the manager.
"I don't know what the hell that moron [tarado] is talking about me for. I never said anything about him.
"I didn't go overboard in my celebration and it was directed at Gary, not at Ferguson and not at the fans.
"I think he did the wrong thing because I was his team-mate and I never said anything bad about him."
The row has made plenty of headlines and has done little to help the FA's hopes of reducing tensions between the clubs.
And Greater Manchester Police assistant chief constable Ian Hopkins has called for fans to be on their best behaviour, with around 9,000 City fans expected at Old Trafford.
He said: "As one of the host cities for the 2018 World Cup bid, the second leg truly is a great day for Manchester to shine. We would ask that fans play their part by behaving sensibly and do the city proud.
"I would like to stress that although the rivalry has always been there between the fans, previous derby matches have passed off largely peacefully and without major incident.
"I would ask that fans adhere to this tradition on Wednesday, regardless of what happened in the first leg."
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