The rapid winger has been in sparkling form for CSKA so far this season and it seems that it has not gone unnoticed to the Premier League pair.
Musa's natural pace and desire to run at defenders means that he is a weapon for any side and both Spurs and West Ham have identified him as someone who could enhance the quality of their squads.
The wide-man has scored eight goals in 23 games across all competitions for CSKA this campaign and, therefore, the Russian club value him highly.
Musa apparently will not leave on a cheap deal, but Spurs and West Ham will both have money to spend in the new-year.
The London duo are competing for places in the top-four and they are determined to strengthen their bids at the next opportunity.
Musa would certainly be an eye-catching addition and would make a statement for either side.
Spurs are expected to have a major overhaul of their squad in January and with Aaron Lennon and Andros Townsend both reportedly up for sale, the signing of a winger is likely to be a priority.
West Ham, meanwhile, are looking for players who can increase the quality of service to their strikers.
Andy Carroll, Diafra Sakho and Enner Valencia have all been in fine form throughout the campaign so far, but Stewart Downing has shouldered much of the side's creative responsibility and Sam Allardyce is looking to relieve some of the pressure on the England international.
Musa still has two years remaining on his deal at CSKA, meaning the Russian club are under no pressure to sell him.