The Argentine U20 international has impressed in his debut season in Serie 'A', scoring nine goals in 25 appearances for Delio Rossi's side.
His form has attracted attention from a host of other clubs in Italy, with Napoli and Juventus also believed to be monitoring his development at Stadio Luigi Ferraris.
Meanwhile, Citizens boss Roberto Mancini is equally keen to sign Icardi, as he continues his search for a replacement for Mario Balotelli, who left the Etihad Stadium in January to sign for AC Milan.
The 20-year-old former Barcelona youngster has been tipped for a bright future in the game, and could join compatriots Carlos Tevez, Sergio Aguero and Pablo Zabableta at Manchester City, were he to agree a summer switch to England.
However, Inter Milan have emerged as favourites to secure Icardi's signature after it was reported that the Nerazzurri are hoping to arrange talks with Sampdoria before the end of the season.
Mancini is hardly short on striker options at the Etihad, but will look to strengthen his squad this summer as he prepares a renewed push for the Premier League title next season.
The reigning champions have all but given up on this year's race, with local rivals Manchester United 12 points clear at the top of the table, even after Manchester City's 1-0 derby win at Old Trafford on Monday night.