If charged, Lieberman will probably have to step down from his post.
The long-running investigation is examining Lieberman's business dealings.
His lawyer and daughter have also been questioned.
In a statement issued by his office on Thursday, Lieberman said he is "in a hurry to end this inquiry which has gone on for 13 years. The minister co-operated and answered the investigators' questions".
"In any normal country, he [Lieberman] would not have been nominated at all with such suspicions, but in Israel everything is possible"
Gideon Levy of the Israeli newspaper Haaretz
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said: "Lieberman has actually complained about the way that this investigation has been dragged out.
"He says it is having a very damaging effect on his public image and he has filed a petition to the court asking for it all to be speeded up."
She noted that the previous government of Ehud Olmert "was brought down by exactly these kind of corruption allegations".
Lieberman became Israeli foreign minister on Tuesday after weeks of talks during which Binyamin Netanyahu, the new prime minister, brought together a ruling coalition.
He is widely regarded as being a controversial politician with ultra-nationalist views, which have left analysts doubting the possibility of peace between Israel and the Palestinians during his tenure.
Speaking to Al Jazeera, Gideon Levy of the Israeli newspaper Haaretz said: "One way or the other, this [investigation] should come to an end, hopefully soon, because it is impossible to [be] Israel's foreign minister and to be under such heavy suspicion.
"In any normal country, he [Lieberman] would not have been nominated at all with such suspicions, but in Israel everything is possible, and we have to wait and see what will come out of those investigations."