West Ham United spent around £40m last summer so have proved they can attract high calibre signings.
The Canadian international is yet to sign a new deal at Turf Moor, with his contract set to expire this summer. Burnley recently signed Georges-Kevin N'koudou from Tottenham Hotspur, which has alerted clubs towards Arfield's availability.
Sky Sports also suggest that Hammers boss David Moyes has been a fan of the 29-year-old for some time and tried to sign him for Sunderland last season.
Arfield has been a fine servant to Burnley since joining from Huddersfield Town in 2013. He has contributed well in helping the Clarets stay up last season and their rise up the table this time round, but he has stood out more during his two Championship campaigns, where he netted 16 league goals over two campaigns (2013-14 and 2015-16), whereas in 85 Premier League appearances he has only scored five times.
West Ham are an ambitious club, which begs the question as to whether the midfielder is the right fit for the club. In the last three summer transfer windows, West Ham have attracted the likes of Javier Hernandez, Marko Arnautovic, Pablo Zabaleta, Andre Ayew and Dimitri Payet to the club. All of those players have played Champions League football and some have won league titles.
The Hammers are currently linked with Daniel Sturrdige according to the Mail and Andre Schurrle as TalkSport reported. Those deals do not look too far out of West Ham's reach either and would match their ambitions of wanting to climb towards the top half rather than just stave off relegation.
Nevertheless, Moyes' team are still threatened by the drop as it stands and Arfield knows what it takes to survive. The Hammers made a similar signing to Arfield last January. They brought Robert Snodgrass from Hull City but it did not work out for the Scot, who is now on loan at Aston Villa, so there is danger that the same could happen with Arfield, too.