Willian's contract with the Blues is up at the end of the campaign, meaning he can speak to overseas clubs about a summer move. Meanwhile, Barkley has been linked with a loan switch, with West Ham United showing an interest, according to Darren Lewis of the Daily Mirror.
Ahead of Chelsea's trip to Newcastle United in the Premier League on Saturday, Lampard made it clear that both Barkley and Willian will be staying at Stamford Bridge, per Oliver Harbord and Alan Smith of Football.London:
"There's no talk here of Ross Barkley going anywhere. He is our player, he played the last couple of games and he has done very well and because of certain circumstances, Ross hasn't featured as much here.
"But, I have got a lot of faith in Ross. That was just news I heard like everyone else this week and I have no feeling towards it. I am very happy with him.
"... Willian is not going anywhere. We know his contract is up at the end of the season and he is in conversations with the club which is still ongoing. There's no news on that. He is certainly our player."
According to James Olley of the Evening Standard, Lampard is determined to keep Willian at the club, although Chelsea have yet to offer him the two-year extension he wants. Barcelona, AC Milan, Juventus and Tottenham Hotspur are all said to have shown an interest in the winger.
Per Kaveh Solhekol of Sky Sports News, the Brazilian has made it clear he would like to stay at Chelsea for a long time:
Chelsea writer Mark Worrall said he would like to see Willian stay but thinks Barkley would benefit from a transfer:
Mark Worrall @gate17marco
Willian & Barkley... Barkley loan to West Ham makes sense. I like Barkley, he can play every week for WHU, he won't at Chelsea & will have a chance of keeping his England place for the Euros. Willian, should be contracted to stay. He is useful this season, end of story. #cfc https://t.co/0EnyxGvhHj
When West Ham boss David Moyes was asked about potential signings in January, he said the club is "not close" to any acquisitions.
Lampard also provided an update on the possible departure of striker Olivier Giroud. "The good thing about Oli is that he is so experienced," he said. "I have a good relationship with him as does the club so again, if all circumstances are right it could happen. While it is not, he is our player."
According to football journalist Fabrizio Romano, the Frenchman is close to a move to Inter Milan:
Chelsea remain in contention for a top-four spot in the Premier League, as well as the UEFA Champions League and the FA Cup this season, meaning Lampard will need a big squad to call upon.
Willian has offered quality and experience to a young Blues side, scoring five goals in 27 appearances across all competitions. Barkley will be hoping to get more opportunities to prove he can be a regular, with only 11 Chelsea appearances to his name so far this season.