The 30-year-old switched back to rugby league with a move to Super League club Catalans Dragons earlier on Tuesday.
Folau was sacked for writing homophobic posts on social media before reaching a settlement with Australia Rugby.
"It did cross our mind, and we have made no approach to Israel Folau," Lenagan told BBC Radio 5 Live.
"We have by now filled our salary cap anyway with very good names, that's the reality."
Folau has signed a one-year deal with the French club, however the Rugby Football League and Super League said they "deplored" Folau's previous comments and said it was "a difficult decision" to allow him into the competition.
Shortly after the deal was released to the public, Wigan announced that their match against Catalans at the DW Stadium on 22 March will be "Pride Day".
The club said they are inviting LGBTQ+ groups to help promote equality in the game.
"[Pride Day] Is a purposeful choice we made today when we heard what had happened," Lenagan went on to tell BBC Sport.
"We felt it was quite important to be proactive, to actually do something even more positively to say to the LGBTQ+ community that we support their environment.
"Rather than being critical of a perceived problem, we thought it was much more important to say 'that is not rugby league, it is a diverse and inclusive sport'."
Folau was sacked for saying "hell awaits" gay people, despite previously being warned over his social media posts.
Asked what Catalans executives thought when informed March's fixture would be a Pride Day fixture, Lenagan said
I just don't understand the thought process behind this from IL. If we didn't make a move as stated then why admit to 'considering it'.
Then why after making that statement take the moral high ground?
Just a weird thing to come out and say.