Oracle sued Google last year, claiming the Web search company's Android mobile operating technology infringes upon Oracle's Java patents.
Oracle bought the Java programing language through its acquisition of Sun Microsystems in January 2010.
Page co-founded Google with fellow Stanford University graduate student Sergey Brin in 1998. The 38-year-old Page, who has a reputation for staying out of the public spotlight, took over as Google CEO in April after a decade under Eric Schmidt.
In a court filing on Thursday, Oracle requested the court's permission to take Page's deposition, saying he made the decision to acquire Android, Inc.
"Mr. Page also participated in negotiations that took place between Sun and Google regarding a Java license for Android and in subsequent communications with Oracle's CEO, Larry Ellison," Oracle wrote in the court filing.
Google has sent a notice that it wants Ellison in a deposition to answer questions under oath, Oracle wrote.
Google called Oracle's request a "harassing demand" because it could get the same information from other sources, according to the filing, which was submitted jointly by both companies.
Oracle waited too long to start taking depositions, and now needs the court's permission to take more, Google argued.
"Oracle should not be permitted to do so," Google wrote in the filing.
Google representatives did not immediately respond to requests for comment, while an Oracle spokeswoman declined to comment.
The case in U.S. District Court, Northern District of California, is Oracle America, Inc v. Google Inc, 10-3561.
(Reporting by Dan Levine and Alexei Oreskovic; Editing by Richard Chang)