The meeting with club president Do Vinh Quang proved unproductive because of disagreement over certain terms in the new contract.
Hai has been willing to extend his contract on the condition he is allowed to play in Europe on loan immediately.
Switzerland is likely to be his destination though many clubs from South Korea, Japan and Latvia have also made offers for him.
The club did not agree to his condition and said they need more time to consider it.
Hai is the most successful player in Vietnamese football history. At 24, he has won just about every national and regional title including three V. League titles, two National Cups, the Vietnam Super Cup, the Vietnam Golden Ball award, the AFF Cup, a SEA Games gold medal, and an Asian U23 silver medal.
He was also a key cog in the Vietnamese team that made a historic entry into the final round of World Cup qualifiers.
In six seasons with Hanoi, he played 125 games and scored 34 goals.
The current contract ends on his birthday, April 12.
Hai has said that while he will earn a lot of money if he continues in Vietnam, he wants to experience a higher level of football.
It was reported that during the negotiation, Hai demanded a monthly salary of VND400 million (US$17,470), but both sides have denied this. This salary is unprecedented in the history of Vietnamese football.
He earns a total of VND500-600 million a month, but it also includes incentives and bonuses, endorsements, and a personal bonus from club owner Do Quang Hien.