Pochettino has emerged as one of the possible candidates to replace Emery, who is currently overseeing a poor run of results.
The Gunners are currently eighth in the Premier League, eight points off the top four.
Pochettino led Spurs to four successive top-four finishes and the Champions League final last season, before losing his job last week.
Neville, speaking to Sky Sports, said:
“Mauricio Pochettino will get linked with every single job in the next three months.
“I think he is in a position where he can select where he goes next, he’s in a strong position and his next job will be one of the super clubs in Europe.
“Arsenal would be interesting. It’s happened before George Graham going the other way. Would Spurs fans like that? Would Mauricio do that? Would Arsenal do that? I’m not sure Mauricio would want to do something like that to Spurs.
“Taking over at Arsenal would be similar to the job he just left at Tottenham, in the sense that there is some investment and spending, but it’s limited.
“He’s not going to go to Arsenal and win the league in the next two years. Whatever the next job Mauricio takes, he will want to win trophies, that will be the most important factor in the decision.”