Pompey chief executive Peter Storrie is due for talks with the 19-year-old's agent to discuss personal terms for the highly rated prospect.
Reo-Coker's agent Tony Finnigan said: "Five Premiership clubs want him and Wimbledon's administrators have agreed a deal with Portsmouth.
"I'm meeting Peter Storrie. I was trying to meet the administrators to discuss Nigel but I'm now meeting them on Wednesday."