St. Paul’s epistle to the Romans was written between A.D. 56 and A.D. 58 (Acts 20:2-3). St. Peter was almost certainly not in Rome when the Epistle was written. All of the Jewish Christian had been expelled from the capital under Claudius and, by A.D. 56 (the second year of Emperor Nero), a few of them were just beginning to return (Romans 16:3). The Christians in Rome are already aware of who Paul is and have been in contact with him for some time (Romans 1:13, 15:22, 16:3-16).
Romans is written to give instruction to the gentile Christians of Rome, not to the Jewish Christians. Paul teaches them because he is the “Apostle to the Gentiles” (Romans 1:5-6, 11:13-14). Ah! But, even though it is Paul who is the Apostle to the Gentiles, these Roman Gentiles were not converted by Paul. Indeed, Paul has never even been to Rome (Romans 1:13, 15:22, etc.). What’s more, Paul directly tells these Roman Gentiles that, now that he has finished preaching in the East, he needs their help to reach, not Italy, but Spain (Romans 15:24). This very same verse (Rom 15:24) tells us that Paul merely hopes to meet the Roman Gentiles “in passing” as he sets out for Spain.
Now, think about this.

Paul, the Apostle to the Gentiles, is going to visit the most important Gentile city in the world - the capital of a world-wide (Gentile) Empire, with over 1 million inhabitants! Yet, he is not going to focus his ministry there, but merely asks for the Roman church’s help to get to Spain. Why would that be?! Well, Paul himself tells us; in Romans 15:20, he writes:
“Thus I aspire to proclaim the Gospel, not where Christ has already been named, so that I do not build on another man’s foundation.”
So, who is this “other man”?

Who is Paul talking about? Again, we are talking about the most important and populous city in the world, the place where “all roads” lead. So, who is responsible for shepherding the church in this most crucial proving ground for the Gospel? If you read the rest of Paul’s writings, whenever he speaks of someone “laying a foundation,” this always refers to the work of an Apostle: Eph. 2:19-20, 1 Cor. 3:10-11, etc… So, what Apostle was associated with Rome? Only one: Simon Peter. Remember, Paul admits that he was never in Rome; nor are any of the other Apostles associated with it. Indeed, Rome is a church composed mostly of Gentiles; and, all throughout Scripture, there is only one Apostle who converted Gentiles as well as Jews. Again, this was Simon Peter.
So, if Peter was not in Rome; if he did not establish the Roman church and hold the status of its bishop (as did Paul in churches like Corinth, even when he was not physically present there - see: 1 Cor. 4:15), then what we are asked to believe is Rome - the most important and populous city in the world at the time - was passed over and ignored by all the Apostles, and entrusted to people with no Apostolic authority. Now that’s unbelievable.