If Raducanu goes deep into the competition, it would end a two year wait after losing the top spot to Boulter in June 2023.
The former US Open winner currently stands at 49th in the world rankings on 1,139 points.
Boulter, meanwhile, is 40th in the world on 1,391 points.
With 390 points available to semi-finalists in Rome, that would see Raducanu reclaim her place at the top of British tennis after a two-year wait.
But Raducanu is not without competition for the top spot as fellow Brit Sonay Kartal remains on the clay.
She sits seven spots behind Raducanu as the world No.56 and faces Linda Noskova on Friday.
Raducanu was in the world’s top ten as recently as 2022, helped by the 2000 points received by players for winning a Grand Slam.
The 22-year-old fought hard to beat Maya Joint 7-5 6-7 (1) 6-3 in the first round of the Italian Open on Wednesday, while Boulter faltered to Anastasia Pavlyuchenkova 6-3 6-3.
Raducanu came close to concluding the match in straight sets but Joint remained strong and won the tie-break 7-1.
