The 25-year-old was acquired from Udinese in 2010, and has since scored 40 goals in 157 appearances, prompting rumours of interest from a number of clubs.
Currently under contract until 2019, Muriel has a release clause of €28m, but Samp President Massimo Ferrero is said to be hopeful for an extension that would see the clause rise to €35m.
Having already approached the player, the same report suggests that Inter are hoping to strike a deal before such a renewal is brokered, and are aiming to lower the amount paid up front through performance-related additions.
The player currently earns €900,000 per season, a figure that would more than double with a move to Inter.
With over four months until the summer transfer window opens, Inter have reportedly agreed personal terms with Muriel, Suning striker Roger Martínez, Wolfsburg defender Ricardo Rodriguez and Roma defender Kostas Manolas. If Ausilio can get these over the line, these would be four good signings.