Leaders Chelsea are hot favourites to be crowned champions, but Ibrahimovic feels United have the potential to win three trophies, while tipping the other sides chasing the Blues to end up empty handed.
The striker played as United defeated Watford 2-0 at Old Trafford on Sunday morning (AEDT) to move within two points of second-placed Tottenham Hotspur, despite remaining sixth in the table.
"We just need to keep going," Ibrahimovic said.
"From five trophies this season, we have won one [the Community Shield] and we are still in four.
"From the teams in front, only one will become champions. The rest will not get a trophy, but we have one and we can get our second one [the EFL Cup] and we are still in the Europa League and FA Cup.
"So if we don't become champions in the Premier League, at least we can try and win two or three trophies.
"We know where we are and that we have been stuck in the same position for many months. We know what we need to do. We need to keep winning to climb in the table and hope the others lose points and we can go past them."
United's UEFA Europa League campaign resumes on Friday (AEDT) with the home first leg of their last-32 tie against Ligue 1 team Saint-Etienne.
"We want to go through the Europa League and we have a good game at home against Saint-Etienne," Ibrahimovic said.
"It is two games, two finals. It doesn't matter if we get a good result on Thursday - we need to have good results in both legs."