Although Quantum chiefs are confident that a major investment deal for it to take a 35 per cent stake in the team will go through imminently, Lotus is still waiting for the money to arrive.
Hulkenberg has been linked with a move to the team, but the German has made it clear he does not want to wait too long as he risks losing all his chances of a good seat for next year.
Hulkenberg is being pushed to complete options he has at Force India and Sauber, while Lotus could risk losing its alternative option of Pastor Maldonado and his Venezuelan backers if it does not decide soon.
Boullier admitted his team wants Hulkenberg to partner Romain Grosjean in 2014, but said he would understand the German driver going elsewhere if Lotus cannot finalise a deal quickly.
"He would like to join us and we would like to have him on board," Boullier said.
"I believe pairing him with Grosjean, it would be one of the best pairings in the pitlane, and a very affordable one - if I may say this!
"I understand his position as well because he had a very bad experience when he was dropped by Williams, and he doesn't want to be in the same situation.
"So I cannot blame him to sign or to commit to someone else if we are late with the timing."
Boullier accepts that there is no guarantee the Quantum will happen, but he thinks the next few days will be crucial in laying out his team's long-term path.
When asked if he expected the situation to be resolved by the Brazilian Grand Prix next weekend, he said: "I hope so. It's what I've been told.
"I've had a promise. So, for the team, for [team owner] Genii, for everybody, it would be great to have this completed."
Boullier said there was still no formal deadline for the deal to happen.
"We have to put in place other plans for the team, and that's going to be the deadline," he said.
"It will be a great reward for the team [if it happens], but also a great reward for Genii Capital who believe in our team and have pushed very hard for the last four years.
"Having this completed, money wise, we would be safe for more than a couple of years.
"You can then work on a proper strategy to establish the team and make everyone in the team reassured about the future."
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