Monalee could head for the Growise Champion Novice Chase at the Punchestown Festival next month after his fine run at Cheltenham.
De Bromhead said: "He went home Wednesday night and he was back in on Thursday morning. Everyone was happy with him at home.
"We were obviously beaten by a very good horse, but it was obviously disappointing for me, although he ran a blinder.
"I don't know what Presenting Percy is going to do, but I would imagine Punchestown is the obvious option for him (Monalee).
"I think three miles around Punchestown would probably be the obvious race to go for. You've got the Ryanair Gold Cup at Fairyhouse, but that is in two weeks' time and that could be a bit soon for him.
"The race at Fairyhouse would be a bit of rush for this lad and I think we are going to stick for in and around three miles, for the time being."
While De Bromhead feels the Ryanair Gold Cup is likely to come too soon for Monalee, he sees it as a possible opportunity for Petit Mouchoir.
The County Waterford handler is thinking of stepping the seven-year-old grey up in distance after he finished third behind the brilliant Footpad in the Arkle Challenge Trophy on Tuesday.
De Bromhead said: "I think Davy (Russell) said that he just went too quick. We are not saying we would have beaten the winner, but we would have finished a fair bit closer.
"I would say we will possibly look at stepping him up in trip for the Ryanair Gold Cup. His race wasn't a slog like Monalee's.
"He is good and, to be honest, the better the ground, the better he is. The one time he beat Footpad it was on better ground.
"I don't think two and a half miles would be an issue for him. He has never done it, but I think it shouldn't be an issue."