Yann Sommer, 37, was the club's first-choice goalkeeper throughout the campaign, making 33 league appearances and keeping 15 clean sheets.
The Swiss goalkeeper's contract with Inter Milan expires at the end of June, and there is currently no indication that an extension will be agreed.
Inter have been searching for a new goalkeeper for next season for some time, with reports suggesting the club was closing in on a move for Ivan Provedel, 32.
Provedel made 27 league appearances for Lazio this season, keeping 12 clean sheets, and holds a contract with the Rome club that runs until the summer of 2027.
Transfer journalist Fabrizio Romano now reports that Inter have reached an agreement with Lazio over a transfer for the goalkeeper.
According to Romano, Inter will pay €3m to sign Provedel, who is set to sign a three-year contract with the Serie A champions.
Romano added that the 32-year-old will serve as Inter's second-choice goalkeeper behind Josep Martinez.
The move represents a significant change in Inter's goalkeeping department, with Sommer's likely departure opening the door for a reshuffle between the posts at San Siro.
Provedel's experience at the top level of Italian football, including a title-winning spell at Lazio under Maurizio Sarri, makes him a credible option to provide competition and cover for Martinez next season.
His arrival would also bring a wealth of Serie A experience to Inter's squad, having established himself as one of the league's more reliable goalkeepers in recent seasons.
Inter's title-winning campaign was built on a strong defensive foundation, and the club's hierarchy are understood to be keen to maintain that level of consistency between the posts as they prepare to defend their Scudetto next season.
The transfer is expected to be finalised once Provedel completes a medical and the formalities of his exit from Lazio are concluded in the coming weeks.
Sommer's expected departure ends a productive spell in Milan, during which the Swiss goalkeeper played a significant role in Inter's recent domestic and European success.
His next destination has not been confirmed, though his experience and continued high level of performance are likely to attract interest from clubs across Europe regardless of his age.
For Lazio, the sale of Provedel represents a notable departure from a goalkeeper who had become a reliable presence in their side, though the move allows the Rome club to bring in a fee for a player approaching the final stretch of his current contract.
Inter's pursuit of defensive reinforcements is not expected to end with Provedel's arrival, with the club continuing to assess further additions as they prepare to defend their title.