Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
Loan pair Sam Hutchinson and Leon Best have extended their deals at Sheffield Wednesday.
The Uruguay international joined the Premier League club in a £12million deal from Bologna last summer and netted five goals in 26 top-flight appearances.
Previously, there was speculation that Fiorentina and AC Milan were monitoring the playmaker's situation, but new potential suitors have emerged - who can offer UEFA Champions League football next term.
Agent Pablo Betancourt told South American radio station Radio Mana Sport: "[Gaston] is currently followed by Borussia Dortmund and Atletico Madrid. At the moment, it is very difficult for him to come back to Italy."
The speculation comes as Ramirez is currently in action with Uruguay in the Confederations Cup, where they are due to take on Brazil in Wednesday's semi-final.