The Foxes are sitting 14th in the Premier League table and are just three points ahead of teams in the relegation zone.
But they are backing themselves to survive in the Premier League this season and the club are already planning for the summer transfer window.
Funds are still tight at Leicester and the club are planning accordingly for the start of next season.
According to Italian outlet FcInterNews.it, Leicester have been in contact with the agent of Inter star Gagliardini.
The 28-year-old midfielder has been a bit part player at Inter this season and is out of contract at the end of the season.
He is set to leave Inter on a free transfer in the summer and his agent has been entertaining approaches.
Leicester have touched base for the midfielder and could make a concrete approach in the next transfer window.
Turkish giants Galatasaray are also interested in Gagliardini and have also contacted his agent.