Seventh-seed Swiatek, the 2020 French Open champion, hit with idol Rafael Nadal at Roland Garros this season.
She then tweeted that her next ideal practice partner would be two-time Wimbledon champion Murray on the grass of the All England Club.
However, with Murray into the third round for the first time since 2017, Swiatek admits that the Briton has other priorities.
"I don't want to bother him during Wimbledon. So maybe we're going to have a chance to do that later or the next tournament, because it's a Grand Slam," said 20-year-old Swiatek.
"I don't want to ruin his routines. I know that playing with a girl is totally different, and it's a different practice for men.
"But he's a really nice guy. We had a few small talks during the tournament. He's down to earth and he's great."
Swiatek had admitted in Paris that she was so star-struck by hitting with Nadal that she arrived on court with a list of conversation starters tucked away in her pocket.
On Friday, the 20-year-old didn't appear to be in desperate need of any help at all, demolishing Romania's Irina-Camelia Begu 6-1, 6-0 to make the fourth round.
Before this week, the 2018 Wimbledon junior champion had won just one match on grass on the main WTA Tour.
She had also been knocked out in the first round of the women's singles on her Wimbledon debut in 2019.
"It's hard to compare my previous years on grass, because in 2019 I was physically weaker," said Swiatek.
"I didn't actually have an idea of how to play on grass. This time it's much, much better, so I just developed overall."
Next up for Swiatek is either 2017 champion Garbine Muguruza or Tunisia's Ons Jabeur.
Results from day 5 of Wimbledon on Friday (x denotes seeded player):
Christian Garín (CHI x17) bt Pedro Martinez (ESP) 6-4, 6-3, 4-6, 6-4
Andrey Rublev (RUS x5) bt Fabio Fognini (ITA x26) 6-3, 5-7, 6-4, 6-2
Karen Khachanov (RUS x25) bt Frances Tiafoe (USA) 6-3, 6-4, 6-4
Karolina Pliskova (CZE x8) bt Tereza Martincova (CZE) 6-3, 6-3
Liudmila Samsonova (RUS) bt Sloane Stephens (USA) 6-2, 2-6, 6-4
Iga Swiatek (POL x7) bt Irina-Camelia Begu (ROM) 6-1, 6-0
Elena Rybakina (KAZ x18) bt Shelby Rogers (USA) 6-1, 6-4
Aryna Sabalenka (BLR x2) bt Maria Camila Osorio Serrano (COL) 6-0, 6-3