There were three Manchester United academy graduates on the pitch at kick-off of the home side's match with the Foxes on Friday night, as Paul Pogba, Andreas Pereira and Rashford were named in the starting eleven.
Asked if wining the league title is a realistic goal for Liverpool, Mellor told LFC TV: "Yes, I think so".
"You also have to consider that Liverpool are City's Kryptonite".
Liverpool splashed the most cash with an outlay of £177m - shelling out £67m on Roma stopper Alisson, in addition to adding Naby Keita (£52.8m), Fabinho (£43.7m) and Xherdan Shaqiri (£13.5m) to their ranks.
The new season gets underway in just two days, with Manchester United hosting Leicester City.
Having been a player at Liverpool, I certainly know that the club and its supporters demand success.
Fulham achieved four top-half finishes during their previous 13-year stint in the Premier League and with the players that they have brought in during the close season, that feat looks well within their powers.
Sarri didn't get off to the best of starts last week as Chelsea were easily brushed aside by Manchester City in the Community Shield. "Premier League clubs' gross player transfer expenditure of £1.2 billion continues to demonstrate the sheer purchasing power of the most commercially successful football league in the world".
It will seem unusual not see the unmistakable figure of Arsene Wenger on the touchline for Arsenal.
'I hope someone can catch them - it would be nice, so hopefully Manchester United can.
'I am sure Jose [Mourinho] has been getting the team right.
His apparent "park the bus" attitude is not what they are used to and this may be his downfall.
The England defender has made no efforts to hide his unhappiness at Spurs over the past year or so, and following a proposed move to Manchester United failing to materialise, the continent could be an escape for the 28-year-old - much like Joe Hart and Torino in 2016.
Whether they can do it across a 38-game season, however, is the big question.
However, out of those three Wolves look the best equipped to stay the distance. The west London club did snap up a player from Madrid on loan for the season: Midfielder Mateo Kovacic, who helped Croatia reach the World Cup final, where it lost to France.