Russian outlet Sport Express are reporting a meeting between themselves and Smolov's agent, Sandor Varga. Varga claimed that Roy Hodgson is interested in Smolov, who currently plays for Russian side Krasnodar.
"They are watching him very closely. He could be a good fit for the Premier League.”
Smolov is currently with Russia at the World Cup, although he is yet to score for the host nation. The 28-year-old enjoyed a successful campaign for Krasnodar, scoring 14 goals and assisting a further six in 24 appearances.
The Crystal Palace manager is reportedly keen to bolster his attack, as his first choice goal scorer, Christian Benteke, struggled greatly last season. He scored three goals in 31 appearances as Crystal Palace endured a challenging campagin.
Smolov has been a transfer target for West Ham previously, with many outlets reporting on failed negotiations between West Ham and Krasnodar in January.
Smolov's agent has mentioned Crystal Palace's interest in his client before, telling Sport Express in January of this year: "West Ham, Crystal Palace - I know for sure that Roy Hodgson is interested in Smolov - and Arsene Wenger asked me about this attacker.
“Another is Everton. In general there are six or seven teams."
Smolov may be available this summer, as he is entering the final year of his contract. He joined Krasnodar on a free transfer in 2015, meaning any offer would generate profit for the Russian side.
Russia will face Spain in the round of 16 at the World Cup, having finished second in Group A behind Uruguay.