The Croatian has been linked with a move to Inter in recent weeks, but with the Nerazzurri expected to keep hold of Miranda, a move to the Stadio Giuseppe Meazza appears unlikely.
Sky Sport Italia reports Roma have entered into advanced talks for Vida, with a deal expected to be completed before the end of the transfer window on Thursday.
The deal is said to be in the region of €7.5m, however other reports suggest it could be a loan deal with an option or obligation to make it permanent.
Vida joined Besiktas in January 2018 on a four-and-a-half-year contract after his previous deal with Dynamo Kiev expired.
Since then, he has netted one goal in 41 appearances for the Turkish side. Vida has also made 71 appearances for the Croatian national team and helped them reach the World Cup Final last summer.