The 23-year-old player, who struggled for regular game time at Bucs during the 2016/17 PSL season, has also been linked with Chippa United and Baroka FC.
Recent reports have indicated that Pirates are open to sending Kutumela out on loan ahead of the July-August Transfer Window.
According to The Citizen source, Abafana Bes'thende are the favourites to sign the promising forward.
“Arrows coach Clinton Larsen has expressed interest in Kutumela from Pirates and, as you’re aware, the two teams have a good working relationship," the source said.
"But don’t rule out a move to Chippa for him because Pirates and Chippa have also been working well together,” the source added.
“But from what I could gather, Arrows are the favourites to land him,” the source concluded.
Bucs defender-come-midfielder Nkosinathi Mthiyane spent the second round of the 2016/17 PSL out on-loan at Arrows.