After looking at the OF options Gallo makes the most sense to me. He's never put up a WAR of 4 so he shouldn't come at too high a cost for the Sox, and he is a lefty that is controlled through 2022.
Also the Rangers must already very familiar with Sox prospects after the Lynn trade.
Lynn put up 7 WAR in 2019. So he is likely valued as more impactful to a team trying to win, but Gallo has the extra half year of control and also the potential for a qualifying which Lynn does not. It will be interesting to see Gallo's market value relative to Lynn's if he is traded, but I don't think the trade values will be that far off. Both players are earning well below free agent market value.