Bale has appeared likely to join Real Madrid all summer, but after Tottenham claimed earlier on Monday that a second club have tabled an offer for the Wales winger, Moyes was quizzed on his interest.
The Scot told Sky Sports: "I said at the start that Manchester United will always be interested in the best players and we'll always be looking to try and improve the team.
"The owners have given me every opportunity to get who I want so we'll continue to look for those players. It's been tough in this window but we're always looking at the best players."
On a stalemate with the Blues, Moyes added: "I thought we played well and I'm disappointed we didn't get a goal. Maybe we lacked a bit of cutting edge with our final pass and final cross.
"I thought Chelsea defended well when they had to. If anybody shaded the best chances, it was certainly us.
"We went with three centre forwards on the pitch and we wanted to try and win the game. We did everything we could and just lacked a ball to get Robin van Persie or Wayne Rooney the chance to score.
"You can play football in many ways. There's nobody who says it has to be done one way. We went out there and tried to win but just couldn't find that final pass.
"It could do with getting cleared up with what is and what isn't a handball because the managers aren't really sure. It was a big call in a big game like this."