Former Manchester United defender Neville believes Solskjaer has a chance to make himself the clear favourite to get the Old Trafford role on a permanent basis.
United were 11 points off the pace in the race for the Champions League when Solskjaer came in but are now ahead with Chelsea and Arsenal both having played the same number of games for the first time. "If the answer to that is yes, then they should give him the job".
A brace from Paul Pogba and a brilliant solo goal from Anthony Martial earned the Red Devils all three points, taking them up to the fourth spot in the league table for the first time this season. Who I meet and when I meet people is not really up for me to tell.
Speaking after an Edinson Cavani penalty earned Thomas Tuchel's men a narrow 1-0 win over Bordeaux on Saturday, Buffon said: 'I appreciated the victory but I did not like the match. The players have responded to him, the fans love him to bits.
"The idea of Ole going through that run of fixtures and coming out of it well, you couldn't sit here conceivably and see another manager".
"What they're seeing, they like".
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Solskjaer confirmed he is making plans for a long-term future at United, as he admitted he is looking beyond the end of this season in case he is given a chance to continue as at Old Trafford.
"It's a different type of questioning".
We would signpost some of the very best moments but Pogba barely put a foot wrong beyond the first 30 minutes.
"He's nearly got a free hit at the moment because it couldn't get any worse in terms of the mood, now it's not just an increased level of happiness but genuinely top performances".
While he felt that speculation of a run for the title was overblown, he said United could still have some influence over who wins the league.