Montiel has claimed worldwide acclaim after scoring the winning penalties in the World Cup and Europa League finals last season - for Argentina and Sevilla.
On top of those successes, Montiel has also won the Copa America with Argentina, as well as the Copa Libertadores with River Plate.
Fabrizio Romano claims that a deal has been reached between the two clubs which will see Montiel move to the City Ground for €11m (£9.4m).
Personal terms are close to being finalised and a medical is scheduled to take place on Monday.
Despite holding his nerve in the biggest of moments, Montiel is not a regular for either club or country.
Club captain Jesus Navas remains ahead of the 26-year-old at Sevilla, while Atletico Madrid's Nahuel Molina is preferred at international level.
However, experience at the very top level should be of great use to Steve Cooper and his side, as Forest look to maintain their place in the Premier League this season.
After an inspired performance in their 2-1 win over Sheffield United on Friday, registering two assists, this news may add legitimacy to the rumours surrounding Serge Aurier's future.
A move to Saudi Arabia has been touted for the Ivorian, even though he only signed a new one-year contract with the club earlier this summer.
Further cover may be needed at right-back too, considering that Ola Aina has been used as a left-back given their current lack of options there.
In addition to that, Aina may be off to the Africa Cup of Nations with Nigeria midway through the season, giving Cooper another potential headache.
Financial difficulties have seen Sevilla make their entire playing squad available for transfer this summer, and Montiel looks set to be the next name to depart.
Goalkeeper Bono completed a move to Al-Hilal earlier this week, shortly after Sevilla were beaten on penalties by Manchester City in the UEFA Super Cup.
Fellow Argentine full-back Marcos Acuna has also been heavily linked with a move to Aston Villa, meaning the two club and international teammates could come up against one another in the Premier League this season.