Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
Villa have been able to complete deals for the likes of Carlos Sanchez, Joe Cole, Philippe Senderos and Aly Cissokho this summer, but quality additions will always be welcomed.
Lambert is, however, aware that he cannot force the issue.
With owner Randy Lambert putting the club up for sale, funds will only be released for players who will make a telling contribution.
Lambert said on his plans and the strength of his squad: “If we can do something that is financially good for the club and is the right move as well, then I’d speak with Randy and see what he thinks.
"But when Christian Benteke and Libor Kozak come back, the forward line is going to be really strong.
"We’ll see what happens in the next couple of weeks."
One of those to have already been added to the ranks has been catching the eye, with Colombia international midfielder Sanchez impressing on Saturday after being introduced off the bench in a 0-0 draw with Newcastle United.
Lambert added: “He was fantastic. He’s going to be a massive player and it was great to have Joe Cole on the bench.
“I thought he would give us strength. He was close to starting and it wasn’t about shutting up shop.
“Charles N’Zogbia had been yellow carded and is just back after a year out.
“I’ve got no doubt Carlos will adjust to the pace of it when he finds his feet.
“He’s only trained for a fortnight. For a guy who’s only trained for a fortnight he certainly never looked like it.”