Goal exclusively revealed on Saturday that Arsenal had made an enquiry for the Uruguayan, before cementing their interest with a £35 million bid, while Real Madrid have not made a secret of their interest in the Welsh forward.
Both players were integral to their respective clubs last season - with Suarez scoring 30 goals and Bale notching 26 - and Neville feels an exit for either would spell trouble for the club.
"You have to say if Liverpool lost Luis Suarez, it would be a huge blow," Neville told The Guardian. "It’s important for Liverpool to keep him to send out the message that they want to get back into the Champions League places.
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"I think this year could be tougher for Tottenham to get into the top four because Arsenal will improve greatly from where they were last year.”
The former Manchester United defender also said that his old club will come under the spotlight this season more so than title rivals Manchester City and Chelsea.
All three clubs head into the new season under new management following Sir Alex Ferguson's retirement and the appointments of Manuel Pellegrini and Jose Mourinho at the Etihad Stadium and Stamford Bridge, respectively.
"Everyone will be looking at Manchester United because Manchester City and Chelsea have changed their managers regularly in the last four, five, six, seven years," Neville continued.
"But you look at David Moyes at Manchester United. He’s an experienced manager, who’s earned this opportunity and he’s got a fantastic group of players who know how to win.
"I suppose with Manchester City not as many people are talking about them at this point of the season, which I think is dangerous because they under-performed last year.
"You think about the likes of Sergio Aguero and David Silva and if they hit top form, and Manuel Pellegrini signs a couple more players, they will be really strong.
"Everyone’s looking at [Jose] Mourinho, everyone’s looking at Moyes and City and Pellegrini are probably sat there thinking, ‘We’re okay at this moment. We’re out of the limelight."