Morris is well known to Taylor from his time as manager of the England Under-21 team, a fact that did not escape The Blues player`s agent Jonathan Barnett.
Earlier in the month, Barnett said: "Jody is very close to Peter Taylor, if a chance came to move to Leicester he wouldn't say no."
With Lennon set to move to Glasgow in a £5.75 million deal on Friday, Taylor appears to be scouring the leagues for a suitable replacement and he admitted that Morris is on his short list.
Speaking of his targets, Taylor said: "I have spoken to one or two managers and made a few enquiries about possible replacements for Neil.
"I wasn't sure when things were going to happen with Neil so I won't be able to get anyone in before the weekend.
"But Jody Morris is a player I really like. He has got great ability and is certainly a player that would be in my thoughts without a doubt."
The one stumbling block to any possible move is that Morris has fought his way into the West London side in recent weeks, after earlier hinting that he would move away to seek first team football.
However, with Stamford Bridge boss Claudio Ranieri now utilising his talents, he may wish to fight for his place in the Chelsea team.
Two other players that are rumoured to be on The Foxes` list are Hearts` Colin Cameron and Manchester United`s Jonathan Greening, but both clubs have stated that they are unwilling to sell.
Taylor, meanwhile, has dismissed the possibility of signing Derby County`s Seth Johnson as a replacement for Lennon, but admitted that he would take him if he was not wanted at Pride Park.
"Seth is a different type of player to Neil," Taylor said. "People link me with him because they know how much I rate him.
"That's why I stuck him in the England squad. He is a different player but if Derby don't want him then I'll take him!"
Taylor`s Derby counterpart Jim Smith laughed off any possibility of the England international moving, saying: "Leicester couldn't afford him - and to be honest, I'm not sure Seth would want to go to Leicester."
