Former Manchester City striker Aguero – the Premier League champion's record scorer – has yet to play a competitive game for Barcelona because of a calf injury.
The Argentinian was in Koeman's thoughts, however, ahead of the clash with Valencia at Camp Nou, while Fati appears ready to make his first start of the season.
It remains to be seen whether that comes on Monday (AEDT) or in the UEFA Champions League game with Dynamo Kiev on Thursday (AEDT), or even in the Clasico against Real Madrid next weekend.
Three home games in eight days for Barcelona could go a long way to determining whether Koeman has a future at Camp Nou, with a UEFA Champions League defeat to Benfica and a LaLiga loss to Atletico Madrid before the international break having ramped up pressure on the Dutchman's position.
Assessing Aguero, Koeman said on Saturday: "He has improved a lot lately. He played 20, 25 minutes in Wednesday's [practice] game and it is going well.
"But he lacks the rhythm of the games and a certain physique. He will get that with games. There is a possibility that he will be on the squad list. His quality is not questioned, he can give a lot to this team. Especially up front."
Barcelona has taken 12 points from its opening seven games in LaLiga, meaning it has ground to make up already on the likes of Real Madrid, Atletico and Real Sociedad, each of which stood on 17 points from eight games coming into this weekend, albeit Koeman's men have a game in hand.
Teenage forward Fati is being eased back into the first team after his long-term knee injury absence, with Koeman determined not to rush the young Spain international, while at the same time aware his qualities could be hugely helpful to this Barcelona team.
The shot conversion rate by Barcelona in LaLiga so far this season is 13.6 per cent, its lowest in a single campaign in the top flight since 2007-2008 (13.5 per cent).
"Every day he is doing better because he has been away for a long time," Koeman said of Fati. "You have to think with Ansu that there are three games this week and he cannot play the entire three games. We must decide what is best for him and the team."
Koeman was backed by president Joan Laporta before the Atletico game, but he needs results and knows it.
"I always try to be calm, which isn't easy," Koeman said. "The important thing is to put your energy where you have an influence. Winning games and points is what counts."
The former Ajax and Everton boss will hope Barcelona's reasonably strong recent record against Valencia can continue. It has lost only one of its past 10 LaLiga games against Valencia (W5 D4), a 2-0 setback in January 2020 under Quique Setien.
A flurry of goals would seem likely, given the recent history of this fixture. Valencia is the away team with the most goals at Camp Nou in LaLiga since 2013-2014, netting a remarkable 14 goals in eight games and scoring at least twice in six of those.
Koeman would presumably take a win by any means, whether a scrappy 1-0 or a dramatic and high-scoring affair. A defeat is almost unthinkable, given it would be a third straight loss for the Blaugrana.
Asked about his position and the pressures that come with it, Koeman said: "I am used to it. Don't worry, in a big club there are always things with the coach. Last year they also talked about the coach.
"The president has defended me and supported me. Things are fine as they are, in spite of the fact that every coach has to win games to continue."