Clarets boss was answering questions following the 3-0 defeat at Stamford Bridge.
And with the transfer window closing at 11pm on Wednesday, Dyche admitted he was hopeful of more deals being done.
He said: “Patrick is close. It’s just a few I’s getting dotted and t’s getting crossed.
“There are a number of other things closer too, but we still have to get them over the line, so we’ll wait and see.”
Former England U21 striker Bamford, 22, spent last season on loan at Crystal Palace and Norwich, following previous loan spells at Middlesbrough and Derby County.