Lennon is keen to sign a striker and a midfielder ahead of the transfer deadline and is hoping business can be completed in the next few days to allow him to strengthen his squad.
Speaking after the 2-2 draw against Inverness in the Scottish Premiership, the Hoops boss said: "I'm hoping to get one done in the next couple of days.
"Another player's representatives are in on Monday so I'm hoping to get a deal done on Monday.
"I'm hoping I'll have two in by midweek."
Lennon has been linked with a move for Hull winger Cameron Stewart but a deal appears unlikely.
He said: "There's nothing in that. There is an interest there but there has been no bid made.
"We spoke to his representatives a long time ago but he's had knee surgery recently. I believe he's fit again but we're looking at other options as well."
Any new signings would not be eligible for Wednesday's Champions League play-off against Shakhter Karagandy, as Celtic aim to overturn a two-goal deficit from the first leg.
Georgios Samaras and Kris Commons both missed the visit of Inverness through injury but Lennon is "optimistic" they will be able to face the Kazakhstan champions at Parkhead.
James Forrest and Derk Boerrigter are rated 50/50, while Anthony Stokes is a doubt after scans revealed a grade one calf strain.
Beram Kayal is likely to be sidelined with a groin strain that forced him out of the clash with Caley Thistle, while Virgil van Dijk is nursing a hamstring twinge.
Lennon said: "We are really, really stretched but it is what it is. We've got to get on with it."
Inverness raced into the lead thanks to goals from Aaron Doran and Richie Foran, before Charlie Mulgrew pulled a goal back just before the break and Adam Matthews grabbed a late equaliser.
Lennon said: "It's a mixed bag. I was really disappointed with our first-half display and really pleased with the second half and the character.
"With the players we had out today we were always going to lack a bit of quality in the final third and that proved to be the case.
"I don't want to go back to what we went through last year in terms of dropping points willy-nilly.
"But, for me, that's a point gained because of the situation we were in.
"I felt we could have won the game but after half an hour you're thinking 'can we get a point now?'."
The draw keeps Inverness top of the table and with an unbeaten record so far this season.
Boss Terry Butcher said: "I did cheekily say to the players that it was two points dropped but, when you look at it, we are very delighted with 2-2.
"It keeps us going. We came here top of the league and we are leaving top of the league.
"The other results have gone for us and we are scoring goals. It's wonderful and the journey keeps on going."