The loan deal was initially proposed by Roma, where former Manchester City striker Dzeko, 34, has fallen out with head coach Paulo Fonseca.
Inter are believed to be interested in the deal on the playing side, but it is a complicated one because of their respective salaries and potential loan fee.
Dzeko, who has scored eight goals in 20 appearances for Roma this season, continued to train alone on Thursday despite being fit after a minor injury.
Chile forward Sanchez, 32, has scored two goals in 19 appearances for Inter, who sit second in Serie A and three points ahead of Roma.