TVNZ has sent political reporter Andrea Vance on the trip to Fiji because of the ban on Ms Dreaver.
Mr Bainimarama has refused to allow media to ask questions of him during Mr Key's trip and will not do any interviews.
Mr Key said he believed lifting the blacklist would be an important step to show Fiji had moved on.
"Freedom of the press is important in any democracy. The reason these people were banned is historic. I think it would be a nice gesture. I can't force them to do it but I do think it would be the right thing to do."
He said Ms Dreaver was "a very significant voice for the Pacific" and was well respected.
In his speech, Mr Bainimarama said the bans were not because he did not like criticism.
"No one who reports on events in Fiji fairly and in a balanced manner is excluded. Any journalist is free to criticise my government or me in an opinion piece or report criticism by others. But we cannot allow wilful propagation of false information which damages the national interest and undermines our wonderful economy. And that is what has happened in the case of certain journalists from New Zealand and others from Australia."
There is still a government-imposed media decree in place in Fiji which requires Fijian media to report in a "balanced" way.
Mr Bainimarama also criticised the wider New Zealand media, saying they appeared to question the legitimacy of his government and were "hostile."