Both Gross and Milner started in the Seagulls' 3-2 defeat against AEK Athens in their Europa League group-stage opener on Thursday night.
However, Milner was withdrawn early in the second half with a suspected muscle injury, while Gross played the full 90 minutes but has also picked up a muscle problem.
Meanwhile, captain Dunk missed the defeat to AEK Athens due to a muscle issue of his own sustained in the 3-1 win at Manchester United last weekend, and teenage striker Ferguson was also absent due to illness.
Brighton head coach Roberto De Zerbi has confirmed that all four players are doubtful for Sunday, with Ferguson the most likely of the quartet to feature in some capacity against Bournemouth.
"I don't know the situation with James Milner," De Zerbi said at a press conference on Friday. "Pascal [Gross] has a muscular problem. We have to analyse the situation and take the best decision.
"With Lewis [Dunk] we can't take any risks (with his muscular problem), especially at this point of the season. With Evan [Ferguson], there's a chance he can play."
De Zerbi added: "I'm more worried about the injuries than the result (against AEK Athens), because we lost against West Ham, a very close game, and then we won against Newcastle and Man United. We have to analyse the quality of the performance, the attitude of the players, not the result."
Asked about the challenges of a busy Thursday-to-Sunday fixture schedule and if he will need to make a lot of changes this weekend, the Italian said: "Yes, a lot. If I analyse the first 11 of Liverpool or Aston Villa or West Ham yesterday, you can find a lot of changes. Especially for us, it is different because we are not used to playing so many games.
"West Ham played in the Conference League last year, Liverpool played in the Champions League, but we are not used to it and we have to change and we have to [use] everyone because we have an alright squad.
"We have to adapt, not only coaches, players - everyone, [including] the people who work inside the club. We do not have many days off in between matches for example. We have to not only organise one game, but we have to organise three games.
"We can't only put our focus on the game tomorrow. With out attitude, behaviour and attention, yes, but we have to work thinking we play every three days and it is totally different. This is my focus."
Dunk, Gross and Milner are all senior leadership figures within Brighton's first-team squad who could miss out this weekend, but De Zerbi has suggested that he has other players who can step up in their absence.
"We have to find another leader," said the Italian. "Gross is a big leader for us. [Danny] Welbeck is another big leader. I think Adam Webster is a leader, one of the best leaders inside the dressing room. He's not had a very good moment in terms of his physical condition, but when he plays, he plays every game in a good way."
"We have a lot of younger players and they have to progress in their leadership, and I am speaking about Billy Gilmour, [Mahmoud] Dahoud, Pervis Estupinan. Pervis is young but he has the potential to be another leader."
Brighton have accumulated 12 points from a possible 15 available in the Premier League this season, and they could move into the top four with a victory over Bournemouth, who are still searching for their first win of the new campaign.