They want an answer within the next fortnight with Arsenal, West Ham and Newcastle circling.
Boss Lennon - with Johan Mjallby and Alan Thompson also back as coaches - revealed: "The talks were very positive. I think Sol enjoyed it.
"It's a good sell, but a hard sell, and he's gone off to think about it.
"It's a harder sell now, with a lack of money, to compete against Premiership clubs.
"What we have in our advantage is the name, the stadium, the support, the history, the chance to win something, to play in Europe, and play on a big stage. Regardless of us being in Scotland, you still get a huge amount of exposure here. I don't think people realise that when they come and see for themselves.
"This would be a huge challenge for Sol as it's a different culture of football. He's been quoted on his concerns about how strong we will be in Europe and I think if we get a few players in before he makes his decision it might turn his head a little bit.
"We could have vetoed his plans for his wedding and honeymoon - but if we did that it would have put a more negative slant on things. In his own mind he's having his wedding and honeymoon and that's it but we might have to talk about that when the time comes.
"For now we just want to get the player on board."