The Bluebirds are without a manager after sacking Dave Jones yesterday following his failure to guide the Welsh outfit to the Premier League.
They are now on the hunt for a replacement and Jenkins admits that former Celtic and Aston Villa boss O'Neill is at the top of the list although they are unsure exactly what the Northern Irishman will cost.
"Martin O'Neill would be on the list of any club. Whether his financial requirements and ours are the same, we'll have to wait and see," he said.
"But we have our options and we'll start meeting people over the next few days.
"It is a tribute to him (Jones) that now it is deemed failure or disappointment that finishing fourth in the Championship is not deemed good enough.
"We have several options on the list. We will see who is available and who is out there.
"We have a list of preferred candidates and the phone didn't stop ringing yesterday (Monday) with people pushing their clients forward so we will have a look at it and try to make a few interviews in the next few days.
"We have sat down with the Malaysian investors over the weekend and had very constructive talks. They are willing to support and there is a budget available."