West Ham are keen on signing the Tottenham winger, also linked with West Bromwich Albion and Everton.
Lennon has been eyed up by Bilic, along with Everton winger Kevin Mirallas. The Hammers have already seen a £6 million approach for Mirallas rejected by the Toffees, and although they are expected to go back in for him, Lennon is an alternative.
The Hammers have become the latest of many Premier League suitors keen on Lennon, with the Birmingham Mail suggesting that he is a target for West Bromwich Albion, whilst the Daily Mail claim he could be heading to Everton this summer - having spent a spell on loan at Goodison Park last term.
Spurs are keen on selling Lennon this summer, and with just one year left on his contract at White Hart Lane, it is likely that they will push through a move should West Ham formalise their interest.
Would Lennon be a good signing for West Ham?
Lennon, 28, is certainly an accomplished player, and would represent a wise replacement for Downing. He is younger than the winger, but more experienced in European competitions, and would likely be a cheap signing.
However, it is hard to imagine him signing for the club as a first-team starter, and he would likely be coming as a replacement for Downing’s substitute role.
Whether Lennon would want that move remains to be seen, but if he was to sign with either Everton or West Brom, it is likely that he would be given far more first-team opportunities than at the Boleyn Ground.