Tottenham Hotspur have been linked with the Crystal Palace winger and the Everton midfielder this summer.
And Jenas believes that Tottenham are waiting for Everton’s and Palace’s asking prices to drop, before making their move.
“Of course, they were never going to go out and buy an Antoine Griezmann or an Angel Di Maria, but I think they do have to make a couple of big signings,” he said.
“ I know names like Ross Barkley and Wilfried Zaha have been mentioned, but the prices for those players has been overinflated so Spurs will probably wait until closer to the end of the transfer window and hope the fee comes down.
“If they don’t, then they simply won’t buy them. Spurs talk a good game, but they do need to add some depth, especially as they will be playing their games at Wembley this season, which won’t make life any easier because every team that plays them at the national stadium will get a real buzz from being there.”
Ross Barkley is known to be available to buy from Everton this summer, but getting a deal over the line for Zaha could be more difficult.
The skilful winger has only recently signed a new deal at Palace, and would cost a considerable sum.
Tottenham have been unwilling to enter the market to date, with Mauricio Pochettino’s side inactivity causing some frustration.
Tottenham are the only Premier League side yet to make a signing, and there are concerns that they could be left behind by some of their title rivals in the upcoming campaign.
Tottenham get their season under way with a match against Newcastle United at St. James’ Park.