You can certainly visit and invite the gentleman at a friendly pace, but his availability will only tell you whether he wishes to continue that friendship. To progress, you need to send a few ambiguous signals. Whether he responds in kind will give you your answer, while still allowing you deniability should he not do so.
For example, you stare at him too long and soulfully, and then look away as if you had hardly known what you were doing. You sit too close to him, and then idly get up and sit somewhere else. You brush up against him as if you had not noticed that you did.
Good luck in the trenches!