The two players were involved in months of talks to extend their contracts amid the Reds' title-winning campaign last season and it has now been revealed Fenway Sports Group came close to walking away from discussions.
Praising sporting director Richard Hughes, Tom told The Athletic in an extract from Walk On: Inside Arne Slot's Liverpool by James Pearce: "My impatience is balanced by his patience.
"I'd call him frequently and say, 'Richard, how are things going with Mo Salah and his contract?', and he would say, 'Tom, it will all be good in the end.'
"I think all the agents who deal with him would say that he conducts business in a very respectful way. He has a plan and he executes it.
"We were delighted that the new contracts for Mo and Virgil were sorted. But you know what? If Richard had called and said, 'The chasm is too big', I would have respected that too. John, Mike and I try to find people who are excellent at their jobs and let them do their jobs.
"We don't meddle, we just provide support and advice from our point of view. There's a lot of trust. I can't say enough wonderful things about Richard."
Despite Liverpool fans' delight when the pair finally signed their new contracts, both Salah and van Dijk have faced criticism amid the side's lacklustre performances this season.
Wayne Rooney recently declaired the pair's attitude a "big concern".
He said on The Wayne Rooney Show: "No-one has seen this coming, it's hit them quick, it's hit them hard and I think they're struggling to find a way out of it.
"This is a time where the manager and the leaders in the team need to figure it out very quickly. Virgil van Dijk and Mohamed Salah, they've signed new deals but I don't think they've really led that team this season.
"I think body language tells you a lot, and I think we're seeing slightly different body language from the two of them. They are the top two players in that team and if their body language is not right, that affects everyone else.
"I might be wrong on this, but if I was a Liverpool fan or the manager, that would be a big concern for me."
