Liverpool owners Fenway Sports Group invited Mourinho to take over at Anfield shortly before Jurgen Klopp was hired in 2015, a report says.
Hosts could not find a way past David de Gea as United held on for a valuable point at Anfield on 14 October.
Klopp upset after Manchester United hold Liverpool to a 0-0 draw at Anfield for the second consecutive season.
Barcelona have made it clear that they are willing to make another move to sign Philippe Coutinho in January, but Klopp remains unconcerned.
Liverpool managed one win in their last seven matches in all competitions. Phil Thompson remains "very confident" the clash between the Reds and Manchester United will be exciting.
Dalglish dismisses criticism of Klopp and urges Liverpool to give him the time he requires to succeed.
Klopp and Mourinho have met each other on seven occasions, with the Portuguese winning only once, in encounters involving both Liverpool and Borussia Dortmund.
England international met Barcelona and Spain legend Xavi while recuperating from thigh injury in Qatar.
Reds are seven points behind United heading into their meeting with United at Anfield on 14 October.
Van Dijk made no secret of his desire to swap Southampton for Merseyside last summer and submitted a transfer request as he attempted to push through a deal.
Mourinho's Manchester United settled for a point at Anfield and Old Trafford against Liverpool. Dalglish claims the Red Devils parked the double decker at Anfield last season.
Virgil van Dijk wanted to join Liverpool, before Southampton reported the Reds. The Dutch defender handed in a transfer request, but the Saints did not sanction his sale.
Only West Ham and Crystal Palace have conceded more Premier League goals than Liverpool this season, but their back four is not to blame.
Jurgen Klopp's former boss and predecessor Eckhard Krautzun has revealed that Manchester United were once the Liverpool manager's desired English club.
The Red Devils have a seven-point advantage over their archrivals heading into the Anfield encounter on 14 October.
Liverpool full-back Andrew Robertson has been backed to start the crucial visit of Manchester United to Anfield this weekend.
Lallana, 29, has been out of action since sustaining a thigh injury in a pre-season game against Atletico Madrid in August.
Liverpool host Manchester United in the lunchtime kickoff on Saturday knowing a defeat would see them slip 10 points behind their rivals.
German midfielder Emre Can currently focused on Liverpool amid growing transfer speculation caused by his ongoing contract stand-off at Anfield.
Reds legend Phil Thompson says Jurgen Klopp must strengthen his defence and bring in a top quality striker.
Liverpool have the third worst defensive record in the Premier League in the 2017/18 season. Manchester United and Manchester City have the joint best record in the league.
Adam Lallana suffered a thigh injury in a pre-season friendly fixture against Atletico Madrid. He has not yet featured for Liverpool this season.