The Sun claim 24-year-old Dack is a target for both clubs as they look to steer themselves away from a Premier League relegation fight come the end of the season.
It is believe Blackburn rate Dack at around the £20million mark, as he continues his sensational start to the season. He has had a hand in 15 goals during his 17 outings this season, scoring 10 and creating five more in assists.
He is regarded as one of the best players in the Championship, but because he is not with a club that are considered one of the biggest in the division, his future is up in the air.
West Ham are likely to want to bring a player such as Dack to the London Stadium in January, with Argentina international Manuel Lanzini still looking to recover from the anterior cruciate ligament injury he suffered in the summer.
But if the Hammers are to land Dack's signature then they will need to beat Roy Hodgson's side to the signing of Dack. West Ham fans reacted to the news their club wanted the Blackburn star in excited fashion.
@WestHamUtd can’t afford to mess this one up amazing player— Oliver Bruton (@olliebruton) December 4, 2018
Please— Aaron Thompson ⚒ (@ThompsWHUFC) December 3, 2018
Get in! Looks quality! Ex Braintree as well— Joe Ashley ⚒ (@realjoeashley) December 4, 2018
Watched him alot at local side Gills, always said I thought a premiership team would gamble on him sooner or later, thought it might be Palace though.— Paul (@PaulLuckhurst) December 4, 2018
Would be more than happy to see if he could step up with us.
I saw Dack play for Gillingham (my local team) many times, he was a cut above the rest in the whole division. Moved to Blackburn and has gone from strength to strength.. we should try and get him before he comes a real star and proves he can do it at the top level.— stevie worboyes (@steviehammer) December 4, 2018