Although Paul is not physically in the same location as the Roman Christians, Paul still cares about them and wants to be with them as part of fellowship. In particular, Paul talked about how Paul and the Roman Christians can "have some fruit" in fellowship (1:13). In the Bible, "fruit" refers to all sorts of character developments, and Paul went into greater detail on fruit in Galatians 5.
As you can see, Paul talks a lot about fellowship with Roman Christians (as well as other Gentiles/non-Jews). In fact, Paul declares himself as "a debtor both to Greeks and to barbarians, both to wise and to unwise" (1:14). The word "debtor" has a literal meaning of "one who pays debt", but in context, Paul used the word as a metaphor for someone with great call and responsibility (like how people in debt are called to pay money in return). And from Paul's comments in 1:15 on how he's ready to share the gospel, the great call and responsibility that Paul has is sharing the gospel (basically what he did Acts 13 onward).
Paul takes his calling really seriously! In a similar way, we are also called to share Jesus (by words and actions).