Weir had a spell in charge of Sheffield United in 2013 but was sacked having won just one his 13 games in charge.
As reported by the Nottingham Post, Weir said: “I wouldn’t say I’ve got aspirations. It’s a really tough job, that’s what I’d say.
“I’ve been an assistant manager for three or four years now at some really good clubs and had some really good experiences.
“But who knows. I’m definitely learning, as you always are in football, trying to make myself and the team better.
“I would never say never, but I’m also conscious that it’s a really difficult job."
After retiring from playing Weir took up a coaching position with Everton, one of his former clubs, and was interviewed for the first-team manager's job in 2013 only for Roberto Martinez to be appointed instead.
Following his unsuccessful spell at Sheffield United, Weir was part of the coaching staff at Brentford and then Rangers prior to joining Nottingham Forest.
Forest are currently in ninth place in the Championship and earning promotion to the Premier League via the play-offs will certainly be a very difficult task.
A commanding centre-back in his playing career, Weir was renowned for his leadership qualities, especially during his time at Everton, and it was anticipated that he could go on to be a successful manager.
However, for now Weir appears comfortable working as an assistant and his concerns about the lack of time given to managers to prove themselves are certainly understandable, with many clubs unwilling to give inexperienced managers time to develop.