The Spain international was touted as a target for United before the Premier League giants moved for Ajax's Donny van de Beek last week.
United great Rio Ferdinand urged Ole Gunnar Solskjaer to sign Saul earlier this year, describing the midfielder as the "conductor" in the Atletico side.
And Saul, who signed a nine-year contract extension with Atleti in 2017, is grateful to have been subjected to such praise from iconic defender Ferdinand.
"I am very flattered that a club like Manchester United, or other teams that ask about me, take me into consideration," he told Marca.
"For me it is very positive. That strong people in those clubs speak well of you means that I am doing things well at Atletico Madrid."
Saul has previously stated he will not consider leaving the Spanish capital while long-serving head coach Diego Simeone is still in charge.
The 25-year-old is entering his seventh season as an Atletico regular and insists the club have nothing to fear when transfer rumors circulate.
"I think not," he said. "[Those feelings] have never been transmitted to me from the club."
Atletico finished 17 points behind LaLiga champions Real Madrid last season, exited the Copa del Rey in the round of 32 and lost to RB Leipzig in the Champions League quarter-finals.
However, Saul is hoping to challenge Madrid and Barcelona for top spot this time around and win his first league title, having been out on loan when Atleti triumphed in 2013-14.
"Honestly, after a complicated season, this one looks exciting and we hope that we will start it well despite the fact that we have little preparation time," he said.
"We have a very good squad, very young, in which we have many things to improve but we are working together and united. I think we have to be ambitious and fight to be up there."
Atletico begin their new season with a home match against Granada on September 26.