After two seasons at Elland Road, the 25-year-old is expected to leave the club this summer, with both Chelsea and Barcelona set to battle for the Brazilian's signature.
Leeds are understood to have accepted a bid worth around £60m from Chelsea to sign Raphinha, while Barcelona are yet to make a formal offer, but club president Joan Laporta has confirmed that they are in talks with the West Yorkshire outfit.
Marsch's men kicked off their pre-season preparations with a comfortable 4-0 win against Blackpool on Thursday, and the American boss provided an update on Raphinha's situation at the club after the game.
Speaking to the Yorkshire Evening Post, Marsch said: "It hasn't been an easy time for [Raphinha] this summer, things have come and gone and there's been a lot of little discussions.
"Right now he's our player, he showed up today and trained with everybody. He had such a good attitude. We had a very open and honest conversation about while he's here he's part of us and we'll see what happens.
"There's still a long way to go in the transfer window, I know he has hopes and dreams and we'll see how everything goes. I said to him, I know he loves this team, this club and being here but we'll see how things progress day by day."
When questioned about whether the attacker will fly with the rest of the squad to Australia for their pre-season tour later this month, Marsch added: "My guess is, I don't know.
"I think we just have to wait and see what happens in the next couple of days. There's urgency from his end I think to come up with a solution and then we have to see where things stand and then make that decision."
Leeds will soon be heading Down Under for three pre-season friendlies against Brisbane Roar, Crystal Palace and Aston Villa, with their first game against the former scheduled to take place on July 14.
Marsch has also revealed that Leeds are "actively hunting a striker" ahead of the 2022-23 campaign and he is keen to bolster his squad further having already signed six players on permanent deals.
The Whites seem to have already recruited a replacement for Raphinha, after they announced on Thursday the arrival of Feyenoord winger Luis Sinisterra on a five-year deal for a fee believed to be worth around £21.5m plus add-ons.