Solskjaer can continue his unbeaten run as Man United manager when they host PSG today.
Neville feels the end of March or start of April would be the best time to announce their permanent boss.
Gary Neville doesn't think it is the right time for Manchester United to announce Ole Gunnar Solskjaer as their permanent manager.
Solskjaer, who replaced Jose Mourinho at the Old Trafford helm, is the bookies' favourite to land the job on a permanent basis after going 11 games unbeaten as interim manager - winning 10 of them in all competitions.
Neville is convinced his former side should decide their permanent boss after the end of a tough run of games against PSG, Chelsea in the FA Cup and a home clash against Liverpool in the Premier League.
However, speaking ahead of the Red Devils' clash against Paris Saint-Germain in the last 16 of the Champions League on Tuesday, the former United captain told Sky Sports: "I think it's too early to give him the job now. I think coming out of March is the right time to appraise it, then look at April with six weeks to go, make a decision considered over a three or four-month period, how the club are feeling, how the players are feeling, and what the results are.
"That's not because they have seven or eight tough games, I just think it's sensible to reflect over a three or four-month period, but Ole Gunnar Solskjaer is putting himself in with a major shout of getting the job.
"If Manchester United continue in this way until the end of the season and get into the top four then the risk with not giving Solskjaer the job would be huge
"If you get to October and they have spent £30m or £40m to get a new coaching set-up into the club and they are fifth, all hell will break loose. People will say: why did you not give Ole the job when he was doing it well?
"I still think you don't need to announce it today because as soon as you do it's 'who are you going to sign and who are you going to get rid of'. At the moment it's still a very good atmosphere, but once the job comes then the questions would start to change.
"He almost had a bit of a free hit when he first came in, but he hasn't just increased happiness, he has brought about top performances."