When reading Romans, can see Paul's desire to go to Rome (which naturally leads to the question, Has the Apostle Paul ever been to Spain? - to which there is no record of it in the Bible). So, to me, the cern of the question depends on the amount of times Paul was in a prison in Rome.
In the 2 Timothy 4:16-17
16 The first time I was brought before the judge, no one came with me. Everyone abandoned me. May it not be counted against them. 17 But the Lord stood with me and gave me strength so that I might preach the Good News in its entirety for all the Gentiles to hear. And he rescued me from certain death.
which points to at least two times in a prison in Rome.
In the book of Acts we read about the three missionary missions and that he was in prison in Caesarea and then in Rome.