The latest name linked is Spanish rising star, Jose Antonio Ruiz – nicknamed Pirulo – a 19-year-old midfielder currently catching the eye with Espanyol's youth team.
His agent, Luis Pacha, has already been in talks with Celtic about the prospect of the former Cadiz player making the move.
But Espanyol have the teenager under contract for the next three years, and would be looking for a fee of around £1million to let him go.
Pirulo is attracting interest from several other clubs, and Celtic will also have to fight off stiff opposition if they are to land Swedish defender Mikael Lustig.
The 24-year-old is out of contract with Rosenborg in January, and this has alerted clubs in Spain and England.
But Lennon watched Lustig play against England last midweek and looks ready to make his move for the man who can play in central defence and at right-back.
Lennon has already made one new signing, handing a contract until the end of the season to former Arsenal midfielder and full-back Andre Blackman.
The 21-year-old impressed in a trial at Lennoxtown and Lennon said: "He's a hungry boy who wants to make a name for himself."