Pogba found the net nine times last season after rejoining United in a then world record £89million deal, with five of those in the Premier League.
That was a creditable return given the France international was often deployed deeper than his preferred position, with greater emphasis on defensive duties than many expected.
But the arrival of midfield anchor Nemanja Matic from Chelsea this summer suggests Jose Mourinho could hand him a more advanced role this term and Red Devils great Giggs expects Pogba to be a regular on the scoresheet.
Speaking at the FA and McDonald’s Community Awards, Giggs said: “I expect Pogba will improve a lot this season. He’s been back a year now and the introduction of Matic is a good buy because it frees him up.
“That’s what you want to see from Pogba, getting on the end of crosses and scoring goals. I think he’s capable of dropping deep or playing in an old-fashioned midfield two but he can get further forward and I expect him to be more effective this year.
“He managed nine last year and hit the crossbar and post plenty of times as well, so he can bring the goals that might turn draws into wins and have a real effect on the team.
“I think both the Manchester sides are the teams to beat this year. It would be silly to dismiss Chelsea after the way they played so dominantly last year but looking at the teams, I think City and United will be up there and the teams to watch.”
United face Real Madrid in the UEFA Super Cup final in Skopje on Tuesday, bringing United into contact not only with Jose Mourinho’s former club, but also with perpetual transfer link Gareth Bale.
The 28-year-old has frequently been linked with a move to Old Trafford in recent seasons and, although the chances of a move this summer appear distant, it is a switch which could one day be on the cards according to fellow Welshman Giggs.
“I don’t think it will happen in this transfer window but you can see it happening one day,” he said.
“If Bale ever comes back to England there are very few clubs who would be able to afford him or he would want to play for. After Real Madrid only a couple of clubs can really compete for prestige or history.
“That’s why the speculation happens every year but I maintain what I’ve always said, I think he’s happy at Madrid. It’s not impossible but he’s playing at one of the biggest clubs in the world and if he’s enjoying himself and playing regularly I don’t see it happening.”