Speaking earlier on Friday, Villa boss Unai Emery confirmed that the 21-year-old is leaving the club, with the Midlands outfit set to include a buy-back clause in the deal which will see the player head to East Yorkshire.
Philogene has passed a medical at Hull and was in the city ahead of the game with Bristol City.
City also have an ongoing interest in Philogene's team-mate Keinan Davis, but there is other second-tier interest.
Rosenior, speaking after his side's 1-1 draw with Bristol City, said: "I think it is a case of dotting the i's and crossing the t's now, which makes me really, really happy.
"Obviously, with every deal, there's so many things, especially with it being a permanent deal that you have to get ticked off.
"But we are really, really close and thank you to Acun (Ilicali) and Tan (Kesler) as it is showing the ambition of the club and what we can achieve this year.
"He is 21 years old and I don't want to put too much pressure on him, but his potential is limitless in terms of his one-v-one ability and I like having wingers and having width in my team and he's someone who completely fits the way we want to play. And he's a great character, which is important for me. I hope we can get that one pushed over the line as it would be a great lift for everyone."
City were chasing a third successive win for the first time in the tenure of Rosenior and first occasion since January 2022 on Friday night.
The wait must go on, but Rosenior is looking at the bigger picture.
Hull took the lead with Ozan Tufan's fourth goal in two home matches, but an impressive Bristol City side, who spurned a lot of chances, levelled just after the hour through Nahki Wells.
He said: "To have seven points from four games, every Championship club would take that at this stage.
"We were 15 seconds from getting a point from Norwich (on the first day) and are not far away.
"I have every confidence we will improve, but we are going to have setbacks and we have a really tough game at Leicester next, which I am looking forward to.
"But if we improve our performance and stay consistent and calm, there's no reason why we cannot have a really good season.
"We could have won or lost the game (v Bristol City). It was a really open game and we move on and hopefully improve.
"It was disappointing (on the night). Whenever you are goal up at home and don't get three points, you have to see it as two points dropped.
"For the first 25 minutes of the game, it was exactly what I wanted to see in terms of control and domination. What happens, which is natural, is that we have a young group.
"We go 1-0 up and the atmosphere in the stadium was top and what we tried to do was score from every attack. What it created was an absolute basketball match which suited Bristol City. We will analyse it as a group in moving forward."
Bristol City chief and former Hull manager Nigel Pearson admitted to being delighted by his side's performance, but was a little perplexed as to why Wells's strike on the stroke of half-time was ruled out for offside after a shot diverted into his path off a home player.
Ahead of this season, the EFL attempted to clarify guidelines for determining a deliberate play by a defender.
If a player is considered to be in control of the pass, attempt to gain possession or clearance, it constitutes a ‘deliberate play’ and any attacking player in an offside position should not be penalised for offside.
Wells celebrated his goal for a number of seconds, before it was eventually ruled out.
On the goal being ruled out, Pearson said: "I've got no idea.
"From the officials' perspective, I thought they let the game go quite freely and there weren't too many problems in that regard.
"With the offside rule, from what we were told this season and from what I've seen since the season has started, there's a bit of confusion and it just needs to be clarified on what the rule is and constituted (in terms) of a deflection into the path of somebody who is in an offside position.
"They (officials) have been put into a position where the rules have been changed and they have had no input.
"They are as exposed to it as we are. I am not having a go, but rule changes have been made and unfortunately, those people who know football have not been included or asked what their opinions are."