Rashford impressed on a season-long loan in Catalonia in 2025/26, scoring 14 goals in all competitions, and winning the LaLiga title.
Hansi Flick had expressed an openness towards bringing Rashford back if a deal could be struck with Manchester United after the 2026 FIFA World Cup.
However, the Spanish giants opted against activating a £30M purchase clause on the 28-year-old, as they looked at other targets in the market.
An £80M deal for Gordon was wrapped up before the World Cup, and Barca focused more attention on getting that agreement over the line, with sporting director Deco claiming it made more sense in the long-term.
"We are extremely grateful to Rashford.
"He contributed a lot last season, but our idea of play is much more linked to Anthony's. His style fits with what the coach is looking for.
"In the case of Gordon, we saw that he was one of the figures we needed.
"We needed more intensity. We analysed a lot of wingers. Signing someone from the Premier League is almost impossible, but Flick was clear in what he wanted and we worked on a deal from there."