The Phillies will send scouts to Baltimore this week, while the Nationals had one at Camden Yards over the weekend, Kubatko added.
This season, Washington ranks second last in bullpen ERA (5.93) while Philadelphia sits 11th worst (4.74) out of 30 teams.
The Orioles are reportedly interested in receiving young prospects from lower levels in any potential trade. They sent right-hander Andrew Cashner to the Boston Red Sox on Saturday in exchange for two 17-year-old prospects from Venezuela - Noelberth Romero and Elio Prado.
Givens has registered seven saves with a 12.8 K/9 rate this season and has a career 3.28 ERA in five years with the Orioles.