Kim Kardashian seems to be nesting with boyfriend Lewis Hamilton as they shop for home goods together

Kim Kardashian seems to be getting serious with boyfriend Lewis Hamilton.

The two were seen heading into a design store to shop for luxury rugs while in Los Angeles on Wednesday afternoon. 

The lovebirds, who were first spotted together at the Super Bowl in February, even matched their attire with similar pale tones as they hinted they may be nesting together in Southern California.

The 41-year-old race car driver, whose primary residence is a penthouse in Monaco, sported a casual look with a cream-colored zip-up pullover with baggy faded blue jeans.

The 45-year-old reality TV star had on a pale gray zip-up jacket with thick leggings from SKIMS that flared at the bottom as she added Perspex high heels and carried a gunmetal gray Gucci shoulder bag with a chain strap.

The stars have been friends for over ten years but their romance only began early this year with vacations in England and France.

During their Wednesday outing, the two did not display any affection as the Formula One driver walked a step ahead of the Keeping Up With The Kardashians star.

He also kept his eyes glued on his cell phone while keeping a low profile in a cap and sunglasses.

Kardashian tried to keep up while in her high heels as she added oversized black sunglasses.

Kim was seen arriving in style in an ivory SUV with a male chauffeur. Later, she was seen walking through a parking lot where a Mercedes-Benz and Range Rover were parked.

Days earlier Hamilton was seen at the Coachella Festival in Indio, California.

The duo were spotted sweetly linking arms as they arrived for Justin Bieber's Coachella set on Saturday. 

The TV personality and her F1 driver boyfriend strolled near the front of the stage during the headlining set. 

The couple - who recently went Instagram official - were also joined by Kardashian's eldest daughter North from her marriage to rapper Kanye West. The 12-year-old wore a long blue wig as they wandered around the festival.

The SKIMS mogul was seen linking arms with Hamilton as they were guided through the crowded grounds to watch Bieber's anticipated performance.

Meanwhile, Ferrari driver Hamilton looked cool in an oversized black sweatshirt which he paired with beige trousers, a white cap, sunglasses and a black bandanna. 

The couple also sent fans wild as they were filmed trying to make a low-key arrival alongside their security team in the VIP area near the stage. 

It comes after Kardashian reportedly made an 11,000 mile round trip just to spend 24 hours with Hamilton.

The reality TV star is believed to have flown to London on Tuesday last week on her private jet to see Hamilton. 

Kardashian is said to have departed Los Angeles on Monday evening and arrived in the UK the following afternoon, local time.

After touching down in Farnborough, Hampshire, she was driven to Hamilton's £18million home in Kensington, west London.

Sources close to Kardashian say her strenuous trip across the Atlantic was a bid to keep their romance alive.

An insider told The Sun: 'Lewis and Kim are two of the busiest people in showbiz, but they are determined to do everything to see each other when they have any spare time. 

'Kim spent Easter weekend with her family and then had a photoshoot in Los Angeles on Monday morning, then flew across the Atlantic to see Lewis.

'They didn't have long together because she had commitments in the US to get back to, but it was quality time.'

The Daily Mail has contacted representatives for both Kardashian and Hamilton.

The day before she landed in London the couple went Instagram official. 

A reel shared by the F1 driver on Monday showed Kardashian sitting in the passenger seat of his red Ferrari.

Hamilton was driving his car at high speeds in Japan.

He set the video to the song Victory Lap by Skepta, PlaqueboyMax and FredAgain and wrote in the caption: 'HERE WE GO AGAIN. TOKYO DRIFT VOL. III.'

Near the end of the video, Kardashian could be seen smiling after Hamilton showed off his driving.

Kardashian recently traveled back to California for an extravagant Easter celebration with her family, but in late March, the pair were seen walking together in Tokyo. 

They were first rumored to be dating in early February when they were seen on what appeared to be a romantic weekend trip in Europe.

They were reportedly spotted in the Cotswolds and later travelled from the UK to Paris.

That same month, they made a public appearance together and were spotted sitting together in the same VIP booth at the Super Bowl.

In early March, they enjoyed a luxurious trip together in Utah, and at the end of the month, the pair traveled to Tokyo alongside Kardashian's kids.

The star reportedly brought along her three youngest children: Saint, ten, Chicago, eight, and Psalm, six. A source previously said that the couple have an 'intense' relationship and added that her family 'adores' him.