Lean toward
Definition 1 of 3
Pro Tip 1/3Preference Nuance
Signals a slight preference rather than a strong commitment. 
He leans toward studying abroad but hasn't decided yet.
Pro Tip 2/3Not Definitive
Shows openness to other options even with a current preference. 
Although she leans toward classical music, she enjoys other genres too.
Pro Tip 3/3Subject to Change
Indicates that a current preference may change over time or with new information. 
They are leaning toward the blue paint, but they might choose a different color tomorrow.