Lijnders made the comments after City’s 4-0 FA quarter-final win against Liverpool last weekend, with Guardiola unable to fulfill media duties as he was serving a touchline ban.
“You never replace a player with the same kind of player because they don’t exist,” said Lijnders.
“But every good story comes to an end, and I hope he enjoys the last months – there are only six weeks – and has a good farewell.”
Silva, a 2017 signing from French club Monaco, made his 450th appearance for City in the EFL Cup victory against Arsenal last month.
The 31-year-old was made club captain last summer following the departure of Kevin De Bruyne.
“He is not the tallest one, the most muscular one, or score 50 goals or make 50 assists a season,” said Guardiola.
“These are the type of players that are spotlighted and everyone talks about. From nine years, I know him quite well and for what a manager requires.
“All managers would say how much they love him because he is incredibly competitive, has a fire inside him always. In the toughest moments and on the biggest stages, he is always there.
“He has been an incredible signing for us, incredible. I love this club and I would love if he could stay and finish his career here but I do not know. He will decide what he will decide. It is his decision.”