Premier League clubs Wolves and Watford are also keeping close tabs on the Braga defender.
The report states that Viano would cost around £10m. (h/t Talk Sports)
Viana, a youth product of Brazilian club Cruzeiro, joined Olympiacos in 2016.
He was then loaned to Braga in 2018.
The Portuguese club decided to snap up the defender permanently after witnessing his talent in a short period.
The 24-year-old has a contract that runs up till 2023.
Viana has been a regular for Abel Ferreira this season, making 27 appearances. Braga are currently fourth in the Portuguese League table.
Why does Leeds need to sign him?
Viana has proved that he is one of the most talented youngsters in the Portuguese League.
His addition would be great for the Whites to reinforce their defence, with Premier League promotion in sight.
Although it is tough to beat the likes of Pontus Jansson and Liam Cooper, Viana would provide adequate cover for them.
Wolves have a strong Portuguese contingent with the likes of Moutinho, Jota, Ruben Vinagre, and manager Nuno Espirito Santo. Citing this reason, the defender could opt for the Wanderers.
LUFC were dealt a huge defeat against Birmingham on Saturday and as a result, they have slipped down to third in the Championship table.
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Marcelo Bielsa will be keen on winning automatic promotion to the Premier League next season.
Leeds will be facing Preston in the midweek Championship fixture.