Several media outlets projected that Republican Dave McCormick would defeat Democratic senator Bob Casey in Pennsylvania, giving Trump's party at least 53 seats in the 100-seat chamber in 2025.
That margin could climb as high as 55 seats if Republicans win close races in Arizona and Nevada, which remain uncalled.
In the battle for the House, Republicans were edging closer to victory on Thursday.
Republicans had secured 209 seats, putting them just nine short of a majority in the 435-seat chamber.
Democrats would have to win 23 of the 31 remaining uncalled races to take a House majority and maintain a toehold on power in Washington.
A final result for Tuesday's election might not be known for some time because 10 of the outstanding races are in California, which typically takes several days to count ballots.
With control of the Senate, Republicans will be in a position to confirm Trump's personnel and judicial appointments, though they will still be short of the 60 votes needed to quickly advance most legislation.
If they control the House as well, they would be able to help Trump deliver on campaign promises like cutting taxes and dramatically restricting immigration.
The other uncalled competitive Senate races are in Nevada, where incumbent Democrat Jacky Rosen led Republican challenger Sam Brown by one percentage point with 94 per cent of the estimated vote counted, and in Arizona, where Democrat Ruben Gallego was leading Republican Kari Lake by two percentage points with 70 per cent of the estimated vote counted.
