The 28-year-old centre-back has long been in agreement over personal terms with the Bundesliga promoted club, but talks with Brighton have so far failed to produce a final breakthrough.
Schalke continue to search for ways to finalise a deal for the Brazilian defender.
Igor joined Brighton from Fiorentina in 2023 and spent last season on loan at Crystal Palace, making little impact on the south coast club's first-team plans this year.
Schalke, promoted to the Bundesliga last season, view the Brazilian as an experienced addition capable of strengthening their backline as they prepare for life back in the top flight.
After recent talk of a possible loan with an obligation to buy, Schalke are now negotiating with Brighton over a loan without a purchase option or obligation, according to Sky.
The Premier League club are said to be hoping that approach will allow the player's market value to increase, paving the way for a more lucrative sale further down the line. It could prove to be the decisive compromise Schalke must accept in their pursuit of the Brazilian.
According to Sky, Schalke want Igor to join them in time for the start of pre-season at the latest. However, Brighton have not yet given the defender clearance to leave, with talks between the two clubs expected to take place shortly.
Brighton have already brought in sufficient cover for Igor, who played no part in their squad last season regardless.
The signings of centre-backs Pascal Struijk, 26, from Leeds United, and Michael Svoboda, 27, from Venezia, have already been officially confirmed.
Brighton are also close to completing a marquee move for Luka Vuskovic, 19, from Tottenham Hotspur.
Elsewhere, Schalke have been linked with left-back Gideon Mensah, 27, who is available on a free transfer after his contract at AJ Auxerre expired.
Journalist Owuraku Ampofo has reported that the Ghana international, who featured at the World Cup, is on the list not only of 1. FC Koln but also of Schalke.
According to Sky, however, there is nothing to those particular rumours.