According to Fabrizio Romano, the exact terms of Ipswich's offer have not been disclosed, though a figure in the region of €40m has been discussed in recent weeks as a possible benchmark for a deal.
Palacios, 27, is understood to be open to leaving the BayArena after six and a half years, with his exit made more likely after Bayer Leverkusen failed to qualify for the Champions League, a shortfall that saw the midfielder accept a wage cut of around a quarter this summer.
His playing time also dipped last season, with 18 Bundesliga appearances and just 12 starts, a drop that may have further encouraged him to consider a fresh challenge. RB Leipzig are also among the clubs credited with concrete interest, alongside further suitors from the Premier League and Bundesliga, meaning Ipswich face genuine competition even after formalising their approach.
Palacios came through the ranks at boyhood club River Plate before joining Leverkusen in January 2020, and has gone on to make 185 appearances for the German club, scoring 15 goals and providing 17 assists, forming part of the side that won a domestic double under Xabi Alonso before Alonso's own departure for Real Madrid.
A regular for Argentina, Palacios has won 41 caps and was part of the World Cup squad this summer, featuring as the Albiceleste reached the final.
Alonso previously praised the midfielder's development in glowing terms, saying the World Cup "helped with his confidence" and that "the better he implements our philosophy and the speed of our game, the better the team will be."
The move would represent one of the most eye-catching signings of Ipswich Town's summer rebuild, with manager Gary O'Neil having already made ten additions to his squad, including Chuba Akpom, Emersonn, Abdul Fatawu and Florentino Luís, as the newly promoted club prepares for a return to the Premier League on the back of three consecutive pre-season wins, most recently a 3-0 victory over Rayo Vallecano.
O'Neil made clear the business is not finished yet.
"We still have a few more to go hopefully," he said. "The plan is to do quite a bit more."