Two proven forwards were said to be on the radar of those at San Siro prior to a change in the dugout being made.
The speculation is unlikely to go away, with serious questions being asked of Lukaku and Sanchez and their ongoing presence at Old Trafford.
Conte is, however, reluctant to be drawn on his recruitment plans after only being in a new role for a matter of hours.
“For sure, we have a plan to try to improve the team.
“But it will be very important for the players, it will be very important to have a great will and great ambition, me, the players and the club, to try to reduce this gap.”
Pressed further on Lukaku and whether Inter have met with the 26-year-old striker and his representatives, Conte said: “No, that’s not right.
“But I repeat in this moment there is a sporting director to talk about this and do this question about the transfer market, about the players.
“But I repeat, now we are very focused to do the first step and to work together.”
Having played down the Lukaku talk, Conte then sought to do likewise with the Sanchez rumours.
It is not only on the arrivals front that Conte is keeping his cards close to his chest, with the Italian also reluctant to be drawn on the future of Inter striker Mauro Icardi.
The Argentine has been linked with a move away from Inter from some time, despite regular claims that he wants to stay.
Asked if he has spoken with Icardi yet, Conte said: “No. I have just started to breathe.
“Every situation we will see and make the best decision with the club. You have to work hard together to make the best decision. The club is the most important thing.”