Mr Jones described the length of time that Welsh Labour leadership contests took as “gruelling” and said they probably did not need to be so long.
Asked if donations could be capped in future, he said: “Clearly we will look at it, but it’s not as easy as that in terms of how these things can be taken forward.
“It is clearly an issue, but we’ll be listening to views in the party to understand how we can improve that process in terms of who should donate, in terms of whether there should full examination of donations, should there be a limit on donations with individuals?”
Labour’s political opponents described Mr Jones’s appointment to lead the review as the party marking its own homework.
But the former first minister said they “misunderstood” what the review was set up to do.
“It is not designed for example to be a kind of separate ministerial code investigation,” he said.
“It is an internal process to look at how the party can better operate internally in any leadership contest that we have in years to come.”
Welsh Conservative Senedd leader Andrew RT Davies said: “How Labour runs its leadership elections is a matter for them, but Vaughan Gething’s donations have implications beyond just the Labour Party.”
Calling for an independent investigation, he added: “Gething’s donations have caused the Welsh Government to stall while our public services suffer as a result of inertia in Cathays Park.”
Plaid Cymru leader Rhun ap Iorwerth urged Labour MSs to support his party’s motion in the Senedd calling for a cap on donations.
He said: “They have the opportunity this week to align themselves with the people of Wales who would not approve of such an eye watering sum of money to one politician.”