City are open to allowing the 28-year-old to leave permanently during the transfer window but sources have told ESPN that they will ask for a fee before sanctioning any move. Steffen is under contract at the Etihad until 2025.
Leicester, according to sources, have registered their interest in Steffen although they have yet to make a formal offer.
He would be reunited with Enzo Maresca at the King Power Stadium after the former City assistant took over as manager following Leicester's relegation to the Championship.
Steffen made 21 first-team appearances during two seasons at the Etihad, collecting Premier League winners' medals in 2021 and 2022.
He was allowed to move on loan to Middlesbrough last season after Pep Guardiola chose to bring in Stefan Ortega as back-up to Ederson last summer.