The midfielder is still battling the hip problem which forced Lennon to leave him out of all but the most important games.
But the player is ready to play through the pain barrier as Celtic prepare for a pivotal run of seven matches in 23 days.
That starts at Perth tomorrow with a lunchtime kick off against St Johnstone which could see the Hoops return to the top of the table. But the main action begins on Wednesday with the Champions League Group G opener against Benfica.
And Brown is ready to lead out the Hoops against the Portuguese league leaders. He said: "I've had two weeks off and I have done pretty much nothing, just rested.
"I'm feeling a lot better. I'll try training today and will see how things go.
"If I can play tomorrow, then I will. If not, then the bigger game is Benfica, and I'm looking forward to it.
"It's up to the manager what he does with me, but I feel I can kickstart now and get back into training."
Having already ruled out Georgios Samaras with the elbow injury he picked up a week ago while playing for Greece, Lennon endured an anxious wait until the rest of his players gradually returned from their international duties.
Adam Matthews suffered toe, hamstring and calf injuries playing for Wales against Belgium last weekend and was replaced at half-time in Tuesday's heavy defeat in Serbia, sounding alarm bells at Parkhead.
But the Hoops' medical staff do not believe the full-back's problems are serious.
Lennon is also hopeful that the Achilles injury which forced Charlie Mulgrew to pull out of Scotland's games against Serbia and Macedonia will also have settled enough to allow him to be in contention tomorrow.
And Joe Ledley, who had to withdraw from the Welsh squad, has also used the break to step up his rehab after injuring his groin playing in Helsingborgs three weeks ago.
New signing Efe Ambrose hopes to be back in Glasgow in time to be included in tomorrow's squad after spending time in Israel this week securing the paperwork required to complete his registration at Celtic.
Another new arrival, Miku, is expected to figure at Perth, though Lennon will check on his condition following the striker's long-haul flight back from international duty with Venezuela.