Swansea manager Graham Potter revealed Wilfried Bony was left out of the squad that overcame Gillingham in the FA Cup because of uncertainty over the striker's future.
Bony, who rejoined Swansea in a £12million deal in August 2017, has been linked with a move away during this month's transfer window.
Turkish club Galatasaray and Al-Sadd, from Qatar, are said to be leading the chase for 30-year-old Ivorian.
Bony cost Manchester City £25m when he joined them from Swansea in 2015 and is understood to be the highest wage earner at the Liberty Stadium.
"Of course there's speculation at this time of year and I thought it was unfair to ask Wilf to be involved," Potter said after a 4-1 win that took Swansea through to the last 16 of the FA Cup in consecutive seasons for the first time since the mid-1960s.
"I thought we would leave it until everything settles down and assess things after the window shuts.
"Wilf has been great with us and perfect with the group, and he wanted to be involved.
"But in the previous round Courtney (Baker-Richardson) scored against Aston Villa and Oli McBurnie's been playing well, so when you add everything up it didn't seem necessary to have him in the squad."
McBurnie claimed his 12th and 13th goals of the season as Swansea went 2-0 up inside 32 minutes.
Josh Rees gave Gillingham hope after the restart but Bersant Celina, with a 25-yard beauty, and Barrie McKay wrapped up secured Swansea's passage to the fifth round in the final 14 minutes.
Asked whether he feared McBurnie's fine form would be attracting envious glances from elsewhere, Potter said: "Regardless of Oli's situation I'll be glad when the transfer window closes.
"As a coach you want to get everything set, know what's happening and talk about football.
"I thought it was a good performance, certainly in the first half, we attacked well and limited them to not much.
"It's a pleasing afternoon, because strange things happen in this competition and it's nice for us that we're through to the next round."
Gillingham's Swansea-born manager Steve Lovell admitted his homecoming had been spoiled by the verve of Potter's side.
Lovell's father was a Swansea season-ticket holder and the Wales forward played for the club in the 1980s.
"I enjoyed it, apart from the result!" Lovell said.
"My dad would have loved to have been here to see this. He put a lot of time and effort into me to become a professional footballer.
"He would have been proud – but also happy as Swansea won 4-1.
"My mum and sister will give me all the pats on the back when I see them, as I need it at the moment."
Lovell said his post-match plan was to have a meal at his mother's house.
"My mum's a Swansea supporter so she may give me a bit more," he said.
"Whatever she cooks I'll eat it as I do as I'm told – even at my age!"
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