The former Chelsea player usually protect their countrymen Uruguay after the incident in October last year.
However, 25 years old and a report on the consideration of a switch of the Ligue 1 giants Paris Saint-Germain after having attracted strong criticism for his behavior in the incident.
And while Poyet has reiterated his desire that Suarez is still in the Premier League, the manager of former Ajax striker gulls fear could leave England in the next transfer period.
When asked if he could leave Anfield Suarez in the final of the season, Poyet said: "Yes, sorry for the Liverpool ...
"He [Suarez was worried about everything that happened was a shock. Oh, he was suffering] is a difficult time. No doubt there is a cultural difference. However, he will adapt.
"I just hope we can keep it in England. I wanted to stay in the UK for English football. If not, you'll lose a lot.
"When you leave - you want to play football, remember that he only wanted to play on the pitch and left and it is difficult to understand because the language because of the work ..
"I'm sure it will show its quality, because everyone knows it's a very good player."
While recent revisions to the forward on French television could have caused speculation about his future, winning the Copa America in 2011, also stressed that he was satisfied with life on Merseyside.
Poyet admits that there were only a handful of prestigious clubs Liverpool, Suarez could move.
He added: "If you leave you can leave something bigger I do not think leaving Liverpool for something smaller and Liverpool are a top club ..
"So we're talking about taking the club, but I'm talking about my opinion here."