The 25-year-old's future at the King Power Stadium is believed to be uncertain as he has just 12 months remaining on his contract.
The Gunners have been linked with a £30m move for the Belgian international, although Mikel Arteta refused to be drawn on speculation when questioned by the media last weekend.
Nevertheless, talkSPORT reporter Alex Crook, via Give Me Sport, claims that "talks have ramped up" between Arsenal and Leicester over a deal for Tielemans, with the Gunners expected to make a bid.
Arsenal have already signed Fabio Vieira from Porto this summer, but Arteta is believed to be an admirer of Tielemans and is keen to bring the former Monaco man to the Emirates Stadium.
Tielemans, who has also been linked with the likes of Manchester United and Newcastle United, has recorded 24 goals and 24 assists in 185 appearances for Leicester across all tournaments, including the winning strike in the 2021 FA Cup final against Chelsea.