Is the Nicene Creed based on the Apostles' Creed?

The Nicene Creed was created during the Council of Nicaea in 325 in order to exclude the teachings of the Alexandrian presbyter, Arius, who taught that the Father and the Son should be considered to be of a different "essence" to each other.

It is likely that a statement in the form, "I believe," or "We believe," was first written during the Council of Nicaea. Eusebius claimed that the Nicene Creed was based on the statement he put forward at that council in the defence of his orthodoxy, hence the "I believe" format. The relationship between the two statements (both of which survive) is clear, although Eusebius' statement of faith was significantly modified in critical places.

Before the time of the Council of Nicaea, the churches appear to have relied upon older traditions as a means of maintaining conformity to the fundamental doctrines of the faith, such as the baptismal questions used in Rome. We know these from Hippolytus' report (mid second century).

The Nicene Creed was not originally intended for ordinary Christians. It was a formal statement intended for bishops.

The Apostles' Creed was for ordinary believers. It does not includes some of the more technical expressions of the Nicene Creed.

The Apostles Creed, for the most part, follows almost exactly the baptismal questions of the church in Rome, as recorded by Hippolytus, and certainly can be considered to represent the set of beliefs taught at Rome at that time to new Christians, and almost certainly much earlier. To move from one form to the other, all one needs to do is to change the emphasis from baptismal questions (that did not have to be learned by heart) to a baptismal declaration of, "I believe," followed by a memorised creed.

Our current Apostles' Creed could have got its name from a letter written in 390, when the Council of Milan referred to the "creed of the Apostles, which the Roman Church has always kept and preserved undefiled." There is certainly nothing in that creed that cannot be found directly in the New Testament.
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Roman Catholic Answer

No, they came from separate sources, different centuries, and for different purposes. The Apostles' Creed is truly ancient and has been used as a symbol at baptism since the very early Church. The Nicene Creed originally came out of the First Council of Nicaea in response to the Arian heresy, and has been used at Mass probably since the fourth or fifth century.
from
The Catechism of the Catholic Church, second edition, English translation 1994

194 The Apostles' Creed is so called because it is rightly considered to be a faithful summary of the apostles' faith. It is the ancient baptismal symbol of the Church of Rome. Its great authority arises form this fact: it is "the Creed of the Roman Church, the See of Peter, the first of the apostles, to which he brought the common faith." (St. Ambrose, Expl symb. 7: J.P. Migne, ed., Patrologia Latina {Paris: 1841-1855} 17, 1196) 195 The Niceno-Constantinopolitan or Nicene Creed draws it great authority from the fact that it stems from the first two ecumenical Councils (in 325 and 381). It remains common to all the great Churches of both East and West to this day.