Howe has emerged as the number one contender to become the next Celtic manager and talks have already taken place between the club and the former Bournemouth boss.
The 43-year-old is still not ready to make a commitment and there are suggestions that he could have offers from the Premier League as well at the end of the season.
Stubbs conceded that Howe can afford to take his time as he knows Celtic want him, but feels from the club’s perspective, they should be nervous as it is clear that the former Cherries manager is their top choice.
He stressed that should Howe reject Celtic, the next manager would be battling questions over being the second choice from the day he takes charge of the Parkhead club in the summer.
The former Bhoy said on the Celtic Huddle Podcast: “From Eddie Howe’s point of view, he is in a very strong position because he is holding all the aces at this moment in time.
“And I think from Celtic’s point of view, it looks like that they have put all their eggs in one basket and they don’t know whether they are going to get their man because he is not prepared to make a decision.
“If I was Dominic McKay or Dermot Desmond, I’d be quite nervous right now because it is out there and public that Eddie Howe is their number one choice.
“And if this doesn’t happen, the next person who comes in and the first question is how do you feel like that you weren’t the number one choice?”
Howe is also believed to be on the radar of Crystal Palace and Newcastle United as well.