The Premier League champions have had a difficult start to the season, winning just twice in their opening six league matches, currently leaving them eight points behind table-toppers Manchester City.
This slow start to the defence of their title could see Chelsea try and strengthen in January, and the Star now says Wanyama will be one of their top targets to come in in midfield, as he is a cheaper alternative to Pogba.
According to reports from the Daily Express towards the end of the summer, the Blues held talks over a possible deal for the French international, but it looks like his transfer fee and wage demands may have been too much for them as the move never went through.
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Wanyama is a similarly powerful and skilful box-to-box player and could be a good buy for Chelsea, although the Star adds that Tottenham are also admirers of his, and may yet look to compete with their London rivals.
Still, with Champions League football on offer at Stamford Bridge, it seems more likely that the Kenyan international would pick a move to west London to help further his career, even if regular games might not be guaranteed due to the presence of players like Nemanja Matic, John Obi Mikel and Ramires in that central defensive role in midfield.