The Daily Mirror says Ibrahimovic, 35, has told his friends that he wants clear evidence that United are building a title-winning squad for next season in order to extend his stay at the club.
The Sweden striker signed a one-year contract with United with an option of an additional year after leaving Paris Saint-Germain last summer.
He is United's leading scorer this season with 28 goals in all competitions.
United are fifth in the league table, four points adrift of the final Champions League qualification spot.
Agent Mino Raiola raised the prospect of Ibrahimovic finishing his career at Italian club Napoli in February, saying the Sweden striker had "always been in love with the city of Naples".
The 35-year-old also has a lucrative offer on the table from LA Galaxy, with the MLS outfit's former general manager Alexi Lalas claiming that the two parties had already held talks over a potential summer move.
Ibrahimovic confirmed last month that his representatives had held discussions on his contract situation with United and spoke glowingly of his working relationship with Red Devils manager Jose Mourinho.
"Let's see what happens, we are talking," Ibrahimovic told the Manchester Evening News.
"I have an option for another year, I want to do great as long as I'm here, so let us see, there is a lot of time."
"I'm enjoying being at a fantastic club, without doubts, one of the biggest clubs in the world with a great coach. I know him before, he's a winner, he's the perfect coach for this club.
"Being a Manchester United player, I don't know how many people have that possibility but I am a Man United player, people wanted me here, I chose the club, I chose the best English club, that's the way it works."