Pochettino's future at Spurs has become increasingly uncertain following a string of comments from the Argentine ahead of talks with chairman Daniel Levy regarding his transfer budget for the summer window.
Chelsea are understood to be monitoring the situation as they search for a replacement for Antonio Conte, but Purslow believes that the rumours are more likely to be a bargaining ploy over a new contract by Pochettino's representatives.
"The financial pressures from the new stadium mean the manager is probably not going to get the kind of level of spending he'd like to see to move Spurs to the next level, and that makes him a target. Obviously it's been long rumoured Chelsea are going to change manager too... but in reality I'm not sure Pochettino would make that move. It's not the most logical move for him if he is going to leave Tottenham Hotspur," he told talkSPORT.
"If contract talks aren't going the way he wants, it would be perfectly natural in the wild world of football for the people around Pochettino to remind Tottenham just how desirable a manager he is, and no club would be more guaranteed to get under Tottenham's skin than potential interest from Chelsea, because that is a very intense rivalry.
"I think Pochettino is well down the track of becoming a Tottenham legend and moving across London to a club which is competing very closely, that isn't a logical move. If I read that Real Madrid or Barcelona were in for him, that might be more credible. Spurs' net transfer spending has been very modest in the Pochettino era, yet they have qualified three times running for the Champions League, so they're doing a tremendous job.
"Club owners and directors put very high value on managers who are able to achieve sustained success with very modest spending. The key word there is success - qualification to the Champions League is one thing, winning trophies is another. It's quite obvious that Pochettino himself would like to put some more silverware in the cabinet and to do that it's also pretty clear that he's going to have to be at a club that competes at the very highest level in the transfer market.
"Right now in English football, that is being dominated by Manchester City and Manchester United. The kind of spending levels those two clubs are putting away explains why they finished first and second in the Premier League this season, and I'm sure no one knows that more than Pochettino."
Current Chelsea boss Conte is expected to leave the club following Saturday's FA Cup final against Manchester United.