The former Real Madrid boss claims that he missed the signature of Henry, who was playing for AS Monaco at the time, by "an inch" as the Frenchman went on to join Juventus in 1999.
"When I was an assistant in Barcelona with Mr [Bobby] Robson in 1996 [we tried to sign him]. He was in Monaco and he went to Juventus, we lost him by an inch," Mourinho told talkSPORT.
The "Special One" says that he did not continue pursuing the striker in future as, according to him, there was no possibility of Henry leaving Arsenal to play for his teams.
"After that he was not on my radar because it was never a possibility to come to my teams. Could you imagine in that moment leaving Arsenal to come to Chelsea? I wouldn't imagine that."
Despite feeling that Henry played okay for the France national team and Barcelona (where he played for three seasons after leaving the Gunners in 2007), Mourinho feels that the striker's best years was in the Premier League, where he managed to score 174 goals from 254 appearances.
"He was OK in Barcelona and the [France] national team, but the real Thierry Henry, the player that we are all going to miss forever, is the one that made unbelievable seasons and incredible history in the Premier League.
"He's the kind of player that you need forever, especially in the Premier League where he was more than any other place."
Meanwhile, Chelsea have been drawn against Liverpool in the two-legged semi-finals of the Capital One Cup, which is scheduled to take place next month.
While Chelsea recorded a 3-1 win over Derby County to book a place in the final four, Liverpool beat Championship leaders Bournemouth by the same scoreline to book a date with the Blues.
Considering the contrasting form of the two sides, Chelsea are the favourites to reach the finals, but Reds boss Brendan Rodgers insists that he is not worried by their League Cup semi-final opponents
"It didn't matter who we got in the draw, it was just important to get there," Rodgers told Sky Sports. "To win this competition you have to win games against big sides."