Lennon revealed on Wednesday night that there had been no movement either way following a failed initial offer for Wolves striker Leigh Griffiths, although he confirmed the club had submitted a bid for another player.
Lennon has other targets, not just up front, but Wolves may be prepared to do business after signing striker Leon Clarke from Coventry for a reported £750,000 fee.
Celtic have made just two signings this month - Icelandic forward Holmbert Fridjonsson and Norway midfielder Stefan Johansen.
Lennon has also demanded answers from Georgios Samaras and Joe Ledley over their futures before the transfer window as the players weigh up new contract offers.
Ross County are aiming to sign 25-year-old Slovan Bratislava right-back Erik Cikos before the deadline in what would be their seventh signing of the month.
And Hibernian have still to tie up a deal to sign Notts County striker Danny Haynes until the end of the season.
Aberdeen have completed their business after signing defender Shaleum Logan on loan from Brentford for the rest of the campaign.
The Dons earlier released Chris Clark following an injury-hit second spell at Pittodrie and sent Josh Magennis on loan to St Mirren for the remainder of the term.
Saints boss Danny Lennon then ended his interest in former Rangers frontman Nacho Novo.
Hearts signed 20-year-old West Ham target man Paul McCallum on loan after succeeding in their application to replace Adam King following the teenager's move to Swansea.
But the Scottish Professional Football League rejected their bid to re-sign Rudi Skacel after Hearts cancelled the playing registration of goalkeeping coach Alan Combe.
There was other good news for Hearts though as Ryan Stevenson committed his future to the club despite receiving a number of offers to go elsewhere.