Reagins said it's now just a waiting game for the Angels, because the offer already has been made to Teixeira and agent Scott Boras.
"We're just waiting on the response," Reagins said. "We think it's a strong offer and a fair offer, so the ball is in their court."
Reagins, who shot down reports that the Angels' top priority would be Ramirez if the club is unable to sign Teixeira, still acknowledged that there is a small chance of Ramirez joining the Angels.
"The chances of that happening are slim, but there is a remote possibility," Reagins said. "Our priorities are elsewhere because we are focused in on Mark."
Angels manager Mike Scioscia, who also was at the event, again said Ramirez would fit in with the club, but he added that Teixeira still takes precedence.
"I think there are plans A, B, C in place to improve our club, but Mark Teixeira is obviously a priority for us," Scioscia said. "But if it doesn't happen, we'll take it one step at a time and see where it leads."
Reagins also said he's confident in his bullpen after losing closer Francisco Rodriguez to the Mets via free agency. The general manager said he likes his in-house options of Jose Arredondo and Scot Shields, and he added that he saw the report of Brian Fuentes' interest in the Angels.
Reagins wouldn't comment further on Fuentes, but it seems as though he's comfortable with the back end of the bullpen.
He also expressed confidence in Kendry Morales, who Reagins said would play first base if the club is unable to reach a deal with Teixeira.
"We're comfortable with Kendry," said Reagins. "He's been outstanding in winter ball, so if we can't come to an agreement with Teixeira, our plan is to move forward with Kendry."