Pulis was commenting after West Brom had picked up a credible 0-0 draw against Everton and he revealed that four bids had been made.
“We have had bids for four different players go in. We will just wait and see," he said to the Birmingham Mail. "We do need a bit of pace out wide without a question of doubt."
West Brom are said by the Birmingham Mail to be interested in Wigan Athletic's Callum McManaman, but Pulis's description of what his side needs makes Lennon a sensible target.
The experienced winger has fallen out of favour at Tottenham, but he still represents a decent option and he would certainly be an upgrade on the Baggies' current squad.
Lennon is said by the Daily Mail to be available for £7 million and, with the 27-year-old having made just two league starts for Spurs this season, a move could be the best option for all parties.