Clarets signed Maxwell Cornet on Sunday.
The Clarets announced the arrival of Ivory Coast international Maxwel Cornet from Lyon before Leeds striker Patrick Bamford rescued his side a point at Turf Moor.
Bamford turned home an 85th-minute equaliser after Chris Wood had given Burnley a second-half lead against his former club.
When asked about more possible new signings, Dyche said: “We’ll see. We’ve worked very hard on Cornet and we’ll see what comes next.
“There’s a couple of ‘maybes’, but they are ‘maybes’ at this stage.”
Cornet has agreed a five-year deal after Burnley paid a reported £12.9million.
Dyche added: “We will see what he can bring. The first thing is for him to settle in to the area, get used to the team and the club.
“We will see that when he gets here and gets used to what we do and first of all we will fitness test him and see where he is at with that.
“Then we’ll see how ready he is on a positional level and then we will look at the varying positions he can play and work out the best position we think he can be effective in for us. First thing’s first, he has got to get in the team.”
When asked if Burnley’s fully-committed approach against Leeds – his side threatened to over-power the visitors early in the second half – gave him hope for the rest of the season, Dyche added: “I think there is optimism anyway and I believe in what we do.
“They are a tricky side to play, Leeds. I thought we contained them pretty well. They had a couple of breakaways and one golden chance and we had a golden chance with Johann (Gudmundsson).
“We took the game on in the second half and I’m aggrieved by Leeds’ goal because I thought it was very unlucky.”
Both Burnley and Leeds are still chasing their first Premier League win of the season, while Dyche’s side remain winless at Turf Moor since January.
Leeds were below-par, but manager Marcelo Bielsa said credit had to be given to the hosts for knocking his players out of their stride.
Bielsa said: “The game, apart from two segments in the middle of each half, we managed to manage it.
“The difference is for us to play well, we need our creative players to be on top of their game. In the case of them, it was a day similar to Everton, but today in a more marked way.
“(Burnley have) three resources that were important: the capacity to force errors and take advantage through two strikers, the management of set-pieces and a very distinct, mechanical style of play.
“The style of play does not demand their players shine. This is something of value when you describe a team.”
Leeds were dealt a blow with both summer signing Junior Firpo and Mateusz Klich ruled out of the match after testing positive for Covid-19.
“They were going to play, but we always have two players in each position ready to play,” Bielsa added.