The Black Country club last night rejected an initial bid from Celtic for the Scottish internationalist but negotiations will continue over the next few days with Lennon warning that the Scottish champions could "move on" if talks stall.
"We may not wait that long," he said of the deal possibly lingering until the transfer deadline on Friday. "We may have options to look at. Preferably we would like to get a definitive answer in the next couple of days."
Griffiths, the former Hibernian and Dundee player, is understood to be keen to join Celtic and Wolves are willing to sell despite their manager Kenny Jackett's public suggestions to the contrary. The League 1 club had a second bid of £500,000 rejected lastnight for Leon Clarke of Coventry City. They also want to offload Bjorn Sigurdarson, the Icelandic forward who has been a disappointment since his £2.4m move from Lillestrom.
The move for Griffiths is thus dependent on factors outwith the control of Celtic but Lennon was keen to add the forward to his squad.
He praised the 23-year-old for his pace, technical ability and goalscoring but conceded the striker may not yet be of the top quality.
Asked if Griffiths was a Champions League striker, he replied: "Maybe not yet. That is up to us to try to turn him into that. Scott McDonald and Gary Hooper went on to play at that level because they got the confidence here. They scored goals and got the elevation into the Champions League. They believed they could play at that level."
Asked about the likelihood of a deal for Griffiths, Lennon said: "You are never confident. Wolves are tough negotiators. We have known in the past when we tried to get Kevin Doyle last year. So I would not say confident. But I am hopeful."
He said, however, that Griffiths was his primary target in this window though another striker could be recruited in the summer.
Lennon also said he would not be encouraging bids for Fraser Forster or Virgil van Dijk who have both impressed this season and who have been linked with other clubs. Similarly, he dismissed reports linking Emilio Izaguirre, the Honduran left-back, with Everton. Bryan Oviedo, the Everton full-back, broke his leg in the FA Cup win at Stevenage at the weekend but Lennon has discouraged Roberto Martinez in any attempt to lure Izaguirre to Merseyside.
"I wouldn't sell him," said Lennon. "I only have one left-back. I don't want to sell any players - the main bulk of the team has been playing consistently now for this season and the previous seasons, and Emilio is a part of that. I have been really pleased with what you might call his resurgence this year. He has been really consistent and played very well in the Champions League.
"You are obviously concerned he might not get back to his previous level when you have an injury, psychologically as much as anything else. But really in the Champions League he really put his mind to it and his qualities shone through."