Kiwomya was placed in charge of first-team affairs after Keith Curle was sacked at the beginning of February. The former Ipswich and Arsenal striker was later that month appointed on a deal for the remainder of the season.
Kiwomya, 43, who is on record as saying he would like the keep the job, has won three and drawn six of his 11 matches in charge.
Magpies chief executive Jim Rodwell told BBC Radio Nottingham: "I'd certainly say he's in pole position for it. I don't think he can be faulted since he got the job.
"I don't think Chris could have done a lot more. He has gone about his business properly and has been diligent.
"We need to sit down with Chris and iron a few things out, I think."
Kiwomya was in charge of the club's development squad before succeeding Curle.