The Times says the Blues are keen on signing Slimani, 29, on loan until the end of the season after growing frustrated with their attempts to sign Andy Carroll from West Ham and Peter Crouch from Stoke City.
Leicester signed Slimani from Sporting Lisbon for a reported fee of £29m ($40m) in August 2016. The Algeria international has only started two Premier League games for the Foxes this season, scoring one goal.
Monaco and Turkish club Besiktas have also been linked with Slimani, with the latter's president watching him in action last week against Fleetwood in the FA Cup.
Chelsea are also considering an approach for Roma's Edin Dzeko, although the former Manchester City striker has already played in the Champions League this season and will be cup-tied for the knockout stages if he moves to Stamford Bridge.
Conte is keen to strengthen his attack as he does not trust Michy Batshuayi to provide capable back up to Morata.
"As you know very well, I think it's not right to talk about players of other teams," the Blues manager was quoted as saying by the Independent when questioned about his interest in Dzeko and Crouch.
"I'm not interested in it. There is a transfer market in this period and if something happens you are the first to know the news.
"I'm not interested in this conversation, also because this is disrespectful for my players, for the other players, for the players of the other clubs."
Chelsea signed Ross Barkley from Everton in a £15m deal earlier this month, with the midfielder an unused substitute in the club's 4-0 win at Brighton on 20 January.
The Blues are third in the Premier League table, 15 points adrift of leaders Manchester City.